Skills Practice Workbook - Glencoe

Skills Practice Workbook 

Contents Include: 

96 worksheets—one for each lesson


Contents Include: 

96 worksheets—one for each lesson

To The Student: 

This Skills Practice Workbook gives you additional problems 

for the concept exercises in each lesson. The exercises are 

designed to aid your study of geometry by reinforcing important 

mathematical skills needed to succeed in the everyday world. 

The material is organized by chapter and lesson, with one skills 

practice worksheet for every lesson in Geometry: Concepts and 

Applications. 

To the Teacher: 

Answers to each worksheet are found in Geometry: Concepts 

and Applications Chapter Resource Masters and also in the 

Teacher Wraparound Edition of Geometry: Concepts and 

Applications. 

Copyright © by The McGraw-Hill Companies, Inc. All rights reserved. Printed in the United 

States of America. Except as permitted under the United States Copyright Act, no part of this 

book may be reproduced in any form, electronic or mechanical, including photocopy, 

recording, or any information storage or retrieval system, without permission in writing from 

the publisher. 

Send all inquiries to: 

The McGraw-Hill Companies 

8787 Orion Place 

Columbus, OH 43240 

ISBN: 0-07-869312-8 Geometry: Concepts and Applications 


1 2 3 4 5 6 7 8 9 10 045 09 08 07 06 05 04

CONTENTS 

Lesson Title Page Lesson Title Page 

1-1 Patterns and Inductive 

Reasoning . . . . . . . . . . . . . . . 1 

1-2 Points, Lines, and Planes . . . . . 2 

1-3 Postulates . . . . . . . . . . . . . . . . . 3 

1-4 Conditional Statements and 

Their Converses . . . . . . . . . . 4 

1-5 Tools of the Trade . . . . . . . . . . . 5 

1-6 A Plan for Problem Solving . . . 6 

2-1 Real Numbers and Number 

Lines . . . . . . . . . . . . . . . . . . . 7 

2-2 Segments and Properties of 

Real Numbers . . . . . . . . . . . . 8 

2-3 Congruent Segments . . . . . . . . . 9 

2-4 The Coordinate Plane . . . . . . . . 10 

2-5 Midpoints . . . . . . . . . . . . . . . . . 11 

3-1 Angles . . . . . . . . . . . . . . . . . . . 12 

3-2 Angle Measure . . . . . . . . . . . . . 13 

3-3 The Angle Addition 

Postulate . . . . . . . . . . . . . . . 14 

3-4 Adjacent Angles and Linear 

Pairs of Angles . . . . . . . . . . . 15 

3-5 Complementary and 

Supplementary Angles . . . . . 16 

3-6 Congruent Angles . . . . . . . . . . . 17 

3-7 Perpendicular Lines . . . . . . . . . 18 

4-1 Parallel Lines and Planes . . . . . 19 

4-2 Parallel Lines and 

Transversals . . . . . . . . . . . . . 20 

4-3 Transversals and Corresponding 

Angles . . . . . . . . . . . . . . . . . 21 

4-4 Proving Lines Parallel . . . . . . . . 22 

4-5 Slope . . . . . . . . . . . . . . . . . . . . 23 

4-6 Equations of Lines . . . . . . . . . . 24 

5-1 Classifying Triangles . . . . . . . . 25 

5-2 Angles of a Triangle . . . . . . . . . 26 

5-3 Geometry in Motion . . . . . . . . . 27 

5-4 Congruent Triangles . . . . . . . . . 28 

5-5 SSS and SAS . . . . . . . . . . . . . . 29 

5-6 ASA and AAS . . . . . . . . . . . . . 30 

6-1 Medians . . . . . . . . . . . . . . . . . . 31 

6-2 Altitudes and Perpendicular 

Bisectors . . . . . . . . . . . . . . . . 32 

6-3 Angle Bisectors of Triangles . . . 33 

6-4 Isosceles Triangles . . . . . . . . . . 34 

6-5 Right Triangles . . . . . . . . . . . . . 35 

6-6 The Pythagorean Theorem . . . . 36 

6-7 Distance on the Coordinate 

Plane . . . . . . . . . . . . . . . . . . . 37 

7-1 Segments, Angles, and 

Inequalities . . . . . . . . . . . . . . 38 

7-2 Exterior Angle Theorem . . . . . . 39 

7-3 Inequalities Within a Triangle . . 40 

7-4 Triangle Inequality Theorem . . . 41 

8-1 Quadrilaterals . . . . . . . . . . . . . . 42 

8-2 Parallelograms . . . . . . . . . . . . . 43 

8-3 Tests for Parallelograms . . . . . . 44 

8-4 Rectangles, Rhombi, and 

Squares . . . . . . . . . . . . . . . . . 45 

8-5 Trapezoids . . . . . . . . . . . . . . . . 46 

9-1 Using Ratios and Proportions . . 47 

9-2 Similar Polygons . . . . . . . . . . . . 48 

9-3 Similar Triangles . . . . . . . . . . . 49 

9-4 Proportional Parts and 

Triangles . . . . . . . . . . . . . . . . 50 

9-5 Triangles and Parallel Lines . . . 51 

9-6 Proportional Parts and Parallel 

Lines . . . . . . . . . . . . . . . . . . . 52 

9-7 Perimeters and Similarity . . . . . 53 

10-1 Naming Polygons . . . . . . . . . . . 54 

10-2 Diagonals and Angle Measure . 55 

10-3 Areas of Polygons . . . . . . . . . . . 56 

10-4 Areas of Triangles and 

Trapezoids . . . . . . . . . . . . . . 57 

10-5 Areas of Regular Polygons . . . . 58 

10-6 Symmetry . . . . . . . . . . . . . . . . . 59 

10-7 Tessellations . . . . . . . . . . . . . . . 60 

11-1 Parts of a Circle . . . . . . . . . . . . 61 

11-2 Arcs and Central Angles . . . . . . 62 

11-3 Arcs and Chords . . . . . . . . . . . . 63 

11-4 Inscribed Polygons . . . . . . . . . . 64 

11-5 Circumference of a Circle . . . . . 65 

11-6 Area of a Circle . . . . . . . . . . . . 66 

12-1 Solid Figures . . . . . . . . . . . . . . 67 

12-2 Surface Areas of Prisms and 

Cylinders . . . . . . . . . . . . . . . 68 

12-3 Volumes of Prisms and 

Cylinders . . . . . . . . . . . . . . . 69 

12-4 Surface Areas of Pyramids 

and Cones . . . . . . . . . . . . . . . 70 

12-5 Volumes of Pyramids and 

Cones . . . . . . . . . . . . . . . . . . 71 

12-6 Spheres . . . . . . . . . . . . . . . . . . . 72 

© Glencoe/McGraw-Hill iii Geometry: Concepts and Applications

Lesson Title Page Lesson Title Page 

12-7 Similarity of Solid Figures . . . . 73 

13-1 Simplifying Square Roots . . . . . 74 

13-2 45°-45°-90° Triangles . . . . . . . . 75 

13-3 30°-60°-90° Triangles . . . . . . . . 76 

13-4 The Tangent Ratio . . . . . . . . . . . 77 

13-5 Sine and Cosine Ratios . . . . . . . 78 

14-1 Inscribed Angles . . . . . . . . . . . . 79 

14-2 Tangents to a Circle . . . . . . . . . 80 

14-3 Secant Angles . . . . . . . . . . . . . . 81 

14-4 Secant-Tangent Angles . . . . . . . 82 

14-5 Segment Measures . . . . . . . . . . 83 

14-6 Equations of Circles . . . . . . . . . 84 

15-1 Logic and Truth Tables . . . . . . . 85 

15-2 Deductive Reasoning . . . . . . . . 86 

15-3 Paragraph Proofs . . . . . . . . . . . . 87 

15-4 Preparing for Two-Column 

Proofs . . . . . . . . . . . . . . . . . . 88 

15-5 Two-Column Proofs . . . . . . . . . 89 

15-6 Coordinate Proofs . . . . . . . . . . . 90 

16-1 Solving Systems of Equations 

by Graphing . . . . . . . . . . . . . 91 

16-2 Solving Systems of Equations 

by Using Algebra . . . . . . . . . 92 

16-3 Translations . . . . . . . . . . . . . . . 93 

16-4 Reflections . . . . . . . . . . . . . . . . 94 

16-5 Rotations . . . . . . . . . . . . . . . . . 95 

16-6 Dilations . . . . . . . . . . . . . . . . . . 96 

© Glencoe/McGraw-Hill iv Geometry: Concepts and Applications

1–1 

NAME DATE PERIOD 

Skills Practice 

Patterns and Inductive Reasoning 

Tell how to find the next term in each pattern. 

1. 7, 12, 17, 22, . . . Add 5. 2. 1, 3, 9, 27, . . . Multiply by 3. 

3. 50, 46, 42, 38, . . . Subtract 4. 4. 10, 20, 40, 80, . . . Multiply by 2. 

5. �4, �1, 2, 5, 8, . . . Add 3. 6. 144, 134, 124, 114, . . . Subtract 10. 

Find the next three terms of each sequence. 

7. 2, 7, 12, 17, . . . 22, 27, 32 8. 100, 93, 86, 79, . . . 72, 65, 58 

9. 11, 22, 33, 44, . . . 55, 66, 77 10. 1, 4, 14, 56, . . . 224, 896, 3584 

11. �2, 4, �8, 16, �32, . . . 64, �128, 256 12. 0, 6, 12, 18, . . . 24, 30, 36 

13. 99, 86, 73, 60, . . . 47, 34, 21 14. 25, 26, 24, 25, . . . 23, 24, 22, 23 

15. 30, 31, 33, 36, . . . 40, 45, 51 16. 5, 10, 20, 40, . . . 80, 160, 320 

17. 220, 210, 190, 160, . . . 120, 70, 10 18. 7, 7, 14, 42, . . . 168, 840, 5040 

Draw the next figure in each pattern. 

19. 

20. 

21. 

© Glencoe/McGraw-Hill 1 Geometry: Concepts and Applications

1–2 



Points, Lines, and Planes 

Use the figure at the right to name examples 

of each term. 1-10. Samples answers are given. 

1. four points four of the following: S, T, M, R, X, Y 

2. two lines �� SX ,YR �� 

3. four segments M�R�, M�S�, M�T�, M�X� 

4. one ray whose endpoint is M �� MY 

5. three collinear points S, M, and X 

6. one point that is not on �� YR S 

7. a segment with points T and M as its endpoints T�M� 

8. a line that does not contain R �� SX 

9. a line containing M �� RY 

10. a segment that lies on �� YR M�R� 

Determine whether each model suggests a point, a line, a ray, a segment, or a plane. 

11. a toothpick segment 12. a floor plane 

13. the tip of a pin point 14. the surface of the water in a swimming 

pool plane 

15. a beam of light from a laser ray 16. fence pole segment 

Draw and label a figure for each situation described. 17-20. Sample 

answers are given. 

17. point K lies on �� RT 

18. plane H contains line a 

R K T 

19. �� AB lies in plane M containing point 20. �� AX and �� AY such that point A is the 

R not on �� AB 

only point common to both rays 

R 

A 

B 

M 

A Y 

© Glencoe/McGraw-Hill 2 Geometry: Concepts and Applications 

X 

a 

H 

S 

Y 

T 

M 

R 

X

1–3 

Postulates 

Refer to the figure at the right. 



1. Name all of the different lines that can be 

drawn through the set of points. 

�� AX , �� AM , �� AC , �� XM , �� XC , �� MC 

2. Name the intersection of �� AX and �� AM . point A 

Name all of the planes that are represented in each figure. 

3. 4. 

R 

V 

W X 

S 

T 

Y 

planes RSTV, SXYT, WXYS, RWSV, planes GXA, XEA, DEA, 

RWXS, VSYT GDA, DEXG 


5. Name the intersection of plane JLM and plane JKL. �� JL 

6. Name the intersection of plane JKO and plane JOM. JO �� 

7. Name two planes that intersect in �� ML . planes JLM and MLKO 

8. Name two planes that intersect in JM �� . planes JOM and JLM 

Determine whether each statement is true or false. If a statement is false, explain why. 

9. If you have two points, then there is only one line that contains both points. true 

10. The intersection of two distinct lines is two points. 

False; two distinct lines intersect at one point. 

11. If you have three noncollinear points, then you have two different planes. 

False; three noncollinear points determine one plane. 

12. A line is the intersection of two distinct planes. true 

13. One point can be the only intersection of two planes. 

False; two planes intersect in a line. 

14. Three planes can intersect in one line. true 


G 

P E 

A 

X 

M 

C 

A 

O 

L 

J 

M 

X 

K

1–4 



Conditional Statements and Their Converses 

Identify the hypothesis and the conclusion of each statement. 

1. If you purchase a computer and do not like it, then you can return it within 30 days. 

Hypothesis—you purchase a computer and do not like it 

Conclusion—you can return it within 30 days 

2. If x � 8 � 15, then x � 7 

Hypothesis—x � 8 � 15 

Conclusion—x � 7 

3. If the drama club raises $2000, then they will go on tour. 

Hypothesis—the drama club raises $2000 

Conclusion—they will go on tour 

4. If the temperature today is 80° or more, then you will go swimming. 

Hypothesis—the temperature today is 80° or more 

Conclusion—you will go swimming 

5. If two lines intersect, then the intersection is a point. 

Hypothesis—two lines intersect 

Conclusion—the intersection is a point 

Write two other forms of each statement. 

6. If two planes intersect, then the intersection is a line. 

The intersection of two planes is a line. All planes that intersect will 

intersect in a line. 

7. If it snows, then you will go sledding. 

You will go sledding if it snows. All people will go sledding on days 

that it snows. 

8. Your dog will be happy if you feed him Doggy Chow. 

If you feed your dog Doggy Chow, then he will be happy. All dogs that 

eat Doggy Chow are happy. 

9. Hiking will be easier if you have hiking boots. 

If you have hiking boots, then hiking will be easier. All people with 

hiking boots can hike easier. 

10. All squares have four sides of equal length and four right angles.. 

If a figure has four sides of equal length and four right angles, then it 

is a square. A figure is a square if it has four sides of equal length 

and four right angles. 

Write the converse of each statement. 

11. If a figure is a triangle, then it has three sides. 

If a figure has three sides, then it is a triangle. 

12. If you find a penny, then you will have good luck. 

If you have good luck, then you found a penny. 

13. If you ride your bicycle recklessly, then you can get hurt. 

If you get hurt, then you rode your bicycle recklessly. 

14. If two distinct lines intersect, then their intersection is one point. 

If the intersection of two lines is one point, then the lines are distinct. 

15. If your cat purrs, then it is contented. 

If your cat is contented, then it purrs. 


1–5 



Tools of the Trade 

Use a straightedge or compass to answer each question. 

1. Which segment is longest? G 2. Which of the three segments at the 

upper right forms a straight line with the 

segment at the lower left? b 

E F G 

3. Does the inner arc or the outer arc on 

the right side of the segments go with 

4. Is C the midpoint of A�B�? no 

the arc on the left side to form part of 

A 

a circle? outer arc 

5. If the circle with center C is drawn 6. If extended, will V�X� intersect Z�Y� at Y ? 

completely, will point X lie on the circle? 

no 

no 

C 

X 


V 

e 

Z 

C 

X 

B 

Y 

a bc

1–6 



A Plan for Problem Solving 

Find the perimeter and area of each rectangle. 

1. 2. 3. 

P � 96 ft, P � 24 cm, P � 4 mi, 

A � 540 ft 2 A � 27 cm 2 A � 1 mi 2 

4. 25 in. 

5. 22 mm 

6. 

P � 70 in., P � 98 mm, P � 16 m, 

A � 250 in 2 A � 594 mm 2 A � 16 m 2 

Find the perimeter and area of each rectangle described. 

7. � � 7 ft, w � 2 ft 8. � � 2 in., w � 1 in. 

P � 18 ft, A � 14 ft 2 P � 6 in., A � 2 in 2 

9. �� 26 cm, w � 23 ft 10. � � 9 mi, w � 1 mi 

P � 98 cm, A � 598 cm 2 P � 20 mi, A � 9 mi 2 

11. � � 7 m, w � 7 m 12. � � 5 yd, w � 25 yd 

P � 28 m, A � 49 m 2 P � 60 yd, A � 125 yd 2 

Find the area of each parallelogram. 

13. 14. 15. 

16 ft 

30 ft 

18 ft 

3 cm 

308 ft2 27 in2 35 mi2 16. 17. 18. 

54 cm 

22 ft 

20 cm 

14 ft 

10 in. 

36 cm 

1 m 

2 m 

1080 cm 2 5 m 2 240 mm 2 

3 in. 

9 cm 

9 in. 

27 mm 


5 in. 

1 mi 

4 m 

8 mi 

5 mi 

5 m 16 mm 

1 mi 

4 m 

15 mm 

7 mi 

17 mm

2–1 



Real Numbers and Number Lines 

Write a real number with five digits to the right of the decimal point. 

1-8. Sample answers given. 

1. an irrational number between 2 and 3 2.43473. . . 

2. a rational number between �2 and �3 with a 2-digit repeating pattern 

�2.57575. . . 

3. two rational numbers between 3 and 4 3.01265 and 3.78659 

4. an irrational number greater than 10 11.12123. . . 

5. a rational number greater than 15 but less than 20 18.97531 

6. an irrational number less than 30 26.54854. . . 

7. an irrational number less than �5 �6.10100. . . 

8. a rational number greater than �8 with a 2-digit repeating pattern 

�6.13131. . . 

Use a number line to find each measure. 

L A Z Q M S T B Y X 

�5 �4 �3 �2 �1 0 1 2 3 4 5 

9. LX 10 10. TX 4 11. ZT 3 12. LZ 3 

1 

1 

13. QM 1 14. MS 1 15. BX 2� 16. BT 1� 

2 

2 

1 

1 

1 

1 

17. ST � 18. LQ 3� 19. BY � 20. AX 8� 

2 

2 

2 

2 

Consider 0.27, 0.27�, and 0.2�7�. 

21. How are these numbers alike? All three numbers are rational. 

22. How are they different? 0.27 � 0.27; 0.27� � 0.277777. . . ; 0.2�7� � 0.27272727. . . 

23. Which number is greatest? 0.27� 

24. How would you read each number? Sample answers: Read 0.27 as 

27 hundredths. Read 0.27� as zero point two seven repeating. Read 0.2�7� 

as zero point two seven all repeating. 


Segments and Properties of Real Numbers 

Three segment measures are given. The three points named are 

collinear. Determine which point is between the other two. 

1. XY � 15, AY � 31, AX � 46 Y 2. AB � 12, BC � 20, AC � 32 B 

3. MO � 75, MC � 34, OC � 41 C 4. DE � 58, GE � 12, DG � 70 E 

5. HM � 2, JM � 1, HJ � 3 M 6. WX � 8, WA � 4, AX � 4 A 

Use the line to find each measure. 

7. If AC � 10 and CG � 21, find AG. 31 

8. If AI � 72 and GI � 11, find AG. 61 

9. If CG � 24 and EG � 14, find CE. 10 

10. If AK � 80 and IK � 24, find AI. 56 

11. If AC � 18 and CK � 72, find AK. 90 

12. If CI � 65 and GI � 13, find CG. 52 

Find the length of each segment in centimeters and in inches. 

13. 

14. 

15. 

16. 

2–2 

13 

2 cm; � in. 

16 

7.6 cm; 3 in. 

7 

1 cm; � in. 

16 

3 

4.5 cm; 1� in. 

4 



A C E G I K 


2–3 



Congruent Segments 

Use the number line to determine whether each statement is true or false. Explain 

your reasoning. 

K L M N O P S T 

�9 �8 �7 �6 �5 �4 �3 �2 �1 0 1 2 3 4 5 6 7 8 9 

1. L�M� is congruent to N�O�. 2. O�S� is congruent to O�L�. 

false; LM � 1 and NO � 3 false; OS � 6 and OL � 5 

3. M is the midpoint of L�N�. 4. P�S� is congruent to N�O�. 

true; LM � 1 and MN � 1 true; PS � 3 and NO � 3 

5. O is the midpoint of L�S�. 6. K�S� is congruent to L�T�. 

false; OS � 6 and OL � 5 false; KS � 14 and LT � 15 

7. P�S� is congruent to K�L�. 8. The origin is the midpoint of K�T�. 

true; PS � 3 and KL � 3 true; the distance from K to the 

origin is 9 and the distance 

from T to the origin is 9 

Determine whether each statement is true or false. Explain your reasoning. 

9. If G�H� � A�Z�, then GH � AZ. true; definition of congruent segments 

10. Every segment has only one midpoint. true; definition of midpoint 

11. A ray cannot bisect a segment. False; a ray is a geometric figure that can 

bisect a segment. 

12. If D�E� � W�X� and W�X� � S�P�, then D�E� � S�P�. True; segment congruence is 

transitive. 

13. If a segment has been bisected, then it is separated into two congruent segments. 

true; definition of segment bisector 

14. If M is the midpoint of A�B�, then A�M� � M�B�. true; definition of midpoint 

15. A plane cannot bisect a segment. False; a plane can bisect a segment. 

16. If points A, B, and C are collinear, then B lies between A and C. False; the order 

of the points may not be A, then B, then C. 

17. A segment can have several midpoints. False; by definition, the midpoint is 

unique, meaning only one. 

18. If Y is between X and Z, then XY = YZ. False; Y does not have to be the 

midpoint of X�Z�. 


2–4 



The Coordinate Plane 

Graph and label each point on the coordinate plane. 

1. Z(0, 5) 2. T(5, �5) 3. B(5, 2) 

4. Q(�3, 3) 5. D(�4, �4) 6. X(0, �4) 

7. M(2, 5) 8. H(�4, 0) 9. F(�3, 1) 

10. R(1, 1) 11. C(3, 4) 12. A(2, 0) 

Name the ordered pair for each point. 

13. R (0, 6) 14. T (0, �5) 

15. Z (�5, 2) 16. B (4, 0) 

17. D (�1, 1) 18. Q (0, �1) 

19. Y (1, �3) 20. M (3, 3) 

21. A (�1, 0) 22. C (2, �5) 

23. Graph x � 2. 

24. Graph y ��1. 

O 

O 

y � �1 

y 

y 

x � 2 

x 

x 


D 

Z 

Q 

y 

Z 

X 

M 

F R 

A 

H O 

D 

y 

R 

A O 

Q 

T 

Y 

C 

C 

M 

B 

T 

B 

x 

x

2–5 



Midpoints 

Use the number line to find the coordinate of the midpoint 

of each segment. 

A D H 

F C E G B 

�6 �5 �4 �3 �2 �1 0 1 2 3 4 5 6 

1. C�E� 2 2. F�C� 0 3. H�F� �2 

4. H�C� �1 5. A�D� �5 6. D�B� 1 

1 

1 

7. C�G� 3 8. G�B� 5� 9. D�H� �3� 

2 

2 

The coordinates of the endpoints of a segment are given. 

Find the coordinates of the midpoint of each segment. 

10. (0, 10), (0, 0) (0,5) 11. (8, 0), (0, 0) (4, 0) 

12. (0, �6), (0, 0) (0, �3) 13. (�20, 0), (0, 0) (�10, 0) 

14. (4, 12), (8, 20) (6, 16) 15. (�2, 3), (2, 5) (0, 4) 

16. (1, �6), (�5, �10) (�2, �8) 17. (�5, �14), (�1, �8) (�3, �11) 

18. (�1, �15), (9, 15) (4, 0) 19. (7, 2), (�7, �2) (0, 0) 

20. (7, �5), (3, 15) (5, 5) 21. (�9, 7), (3, 5) (�3, 6) 

22. (1, 3), (4, 8) �2 , 5 � 23. (�6, 7), (9, 10) �1 , 8 1 1 

1 1 

� 

� 2 

� 2 


� 2 

� 2

3–1 



Angles 

Name each angle in four ways. Then identify its 

vertex and its sides. 

1. 2. 3. 

C 

�AXC, �CXA, �X, �1; X; �MOR, �ROM, �O, �6; �DFH, �HFD, �F, �4; 

�� XA ,XC �� O; OR �� ,OM �� F; FH �� ,FD �� 

Name all angles having A as their vertex. 

4. 5. 5 

6. 

X 

A 

Y 

1 

1 

2 

A Z 

X 

�XAZ, �1, �2 �MAZ, �5, �6 �ABC, �ABD, �EBC, 

�7, �8, �9 

Tell whether each point is in the interior, exterior 

or on the angle. 

7. L 

8. 9. 

on exterior interior 

10. 11. 12. 

B 

M R 

A M 

6 

Z 

on exterior exterior 

O 

6 

P 

Determine whether each statement is true or false. 

13. The figure formed by opposite rays is sometimes referred to as a straight angle. true 

14. The vertex is in the exterior of an angle. false 

15. An angle separates the plane into two parts: the interior and the exterior of the angle. 

false 


C 

X 

B 

D 

9 

7 8 

C 

A 

D 

F 

E 

A 

4 

Z 

H

3–2 



Angle Measure 

Use a protractor to find the measure of each angle. 

Then classify each angle as acute, obtuse, or right. 

1. �TAR 30; acute 2. �BAX 90; right 

3. �CAX 25; acute 4. �TAX 150; obtuse 

5. �BAR 90; right 6. �QAB 20; acute 

7. �RAC 155; obtuse 8. �TAC 125; obtuse 

9. �QAC 85; acute 10. �QAR 65; acute 

11. �QAX 115; obtuse 12. �TAB 60; acute 

Use a protractor to draw an angle having each measurement. 

Then classify each angle as acute, obtuse, or right. 

13. 50° acute 14. 120° obtuse 15. 90° right 

16. 25° acute 17. 100° obtuse 18. 140° obtuse 

19. 10° acute 20. 135° obtuse 21. 85° acute 


T 

R 

Q 

A 

B 

C 

X

3–3 



The Angle Addition Postulate 


1. If m�ABE � 100 and m�ABF � 65, 

find m�2. 35 

2. Find m�4 if m�EBC � 80 and 

m�EBD � 44. 36 

3. Find m�3 if m�FBD � 85 and 

m�FBE � 42. 43 

4. If m�ABE � 105 and m�EBD � 46, 

find m�ABD. 151 

5. If m�ABF � 46 and m�FBE � 54, 

find m�ABE. 100 

6. Find m�FBC if m�2 � 45 and 

m�EBC � 78. 123 

7. If m�FBD � 102 and BE �� bisects �FBD, 

find �FBE. 51 


8. If m�WAZ � 95 and m�ZAO � 40, 

find m�WAO. 135 

9. If �WAZ is a right angle and m�YAZ � 35, 

find m�WAY. 55 

10. If m�XAZ � 82 and AY �� bisects �XAZ, 

find m�YAZ. 41 

11. If m�WAY � 66 and AX �� bisects �WAY, 

find m�XAY. 33 

12. Find m�YAO if m�WAO � 130 and 

m�WAY � 70. 60 

13. If m�WAO � 142, and AY �� bisects �WAO, 

find m�WAY. 71 

14. Find m�XAO if m�XAY � 35, 

m�YAZ � 40, and m�ZAO � 42. 117 

A B 

1 4 

2 3 

C 


F 

W 

E 

X 

D 

Y 

Z 

A O

3–4 



Adjacent Angles and Linear Pairs of Angles 

Use the terms adjacent angles, linear pair, or neither 

to describe angles 1 and 2 in as many ways as possible. 

1. 1 2 

2. 3. 

neither adjacent angles adjacent angles; 

linear pair 

4. 5. 6. 

1 

2 

neither adjacent angles adjacent angles 

7. 8. 2 9. 1 

1 2 

adjacent angles neither adjacent angles; 

linear pair 

In the figure at the right, MA �� and MG �� are opposite 

rays. Also, MC �� and MJ �� are opposite rays. 

10. Which angle forms a linear pair with �AMC? 

�CMG or �AMJ 

11. Do �CME and �EMJ form a linear pair? 

Justify your answer. Yes, their noncommon sides 

are opposite rays. 

1 2 

12. Name two angles that are adjacent to �EMG. 

Sample answer: �CME, �GMJ 

13. Name two angles that form a linear pair 

with �JMG. 

�AMJ, �CMG 

14. Name three angles that are adjacent to 

�AMK. �AMC, �KMJ, �KMG 

1 2 

1 

1 2 


A 

K 

1 2 

2 

M 

C 

J 

G 

E

3–5 



Complementary and Supplementary Angles 

Refer to the figures at the right. 

1. Name a pair of complementary angles. 

�BOD, �DOF 

2. Name two right angles. �BOJ, �BOF 

3. Name three pairs of adjacent supplementary 

angles. �JOB, �BOF; �JOD, �DOF; 

�JOH, �HOF 

4. Find the measure of an angle that is 

complementary to �JOH. 5 


supplementary to �DOF. 147 

6. Find the measure of �BOH. 175 

7. Name a pair of complementary angles. 

�WMR, �RMS or �SMT, �TMZ 

8. Name two right angles. �WMS, �ZMS 


complementary to �YMZ. 58 


supplementary to �WMT. 60 

11. Find the measure of �XMY. 28 

Exercises 7-13 

12. Is �YMT a right angle? Justify your answer. No, its measure is 32 � 60, or 92. 


supplementary to �XMR. 25 

14. Find m�3 if �3 and �4 form a linear pair and m�4 � 55. 125 

15. If �1 and �2 form a linear pair and m�1 � 130, find m�2. 50 

16. Angles DEF and XYZ form a linear pair. If m�DEF � 170, what is m�XYZ? 10 

17. If �4 and �8 are complementary and m�4 � 45, find m�8. 45 

18. If m�3 � 10 and �3 and �7 are complementary, what is m�7? 80 

57° 

O 33° 

85° 95° 


Z 

Y 

J 

T 

B 

H 

D 

Exercises 1-6 

X 

M 

32° 120° 

60° 35° 

55° 

30° 

S 

R 

F 

W

3–6 



Congruent Angles 

Find the value of x in each figure. 

1. 2. 3. 

x° 

152° 

152 58 114 

4. 5. 6. 

(3x)° 78° 

26 25 25 

7. What is the measure of 

an angle complementary to �XYZ 

if �MOR � �XYZ? 42 

48° 

M 

O R 

Use the figure at the right. 

9. If �1 � �3 and m�1 � 64, find the measure of 

an angle that is supplementary to �3. 116 

10. If �AOB is supplementary to �BOC, �BOC 

is supplementary to �COD, and m�AOB � 58, 

find m�BOC and m�COD. 122; 58 

Z 

11. Find the measure of an angle that is complementary 

to �1 if �1 � �2 and m�2 � 75. 15 

Y 

90° 

12. Find the measure of an angle that is supplementary to �4 if �4 � �9 and m�9 � 24. 

156 


58° 

x° 

(4x � 10)° 

X A 

(x � 8)° 

(6x � 15)° 

122° 

45° 

8. OA �� and OB �� are opposite rays 

and OC �� and OD �� are also 

opposite rays. If m�2 � 90 and 

m�1 and � 45, what is m�4? 

45 

C 

A 

O 4 

1 

2 

3 

D 

B 

1 

2 

4 

O 

3 

B 

D 

C

3–7 

Perpendicular Lines 



�� AB ⊥ �� BE ,FC �� ⊥ �� BE , and point X is the 

midpoint of A�C�. Determine whether each of the 

following is true or false. 

1. �XCB � �DCE true 

2. �BCY is a right angle. true 

3. �FCE and �FCX are supplementary. false 

4. �� AB ⊥ �� BC true 

5. �FCD is a right angle. false 

6. �FCX and �XCB are complementary. true 

7. m�WBZ � m�WBA false 

8. �� FC is the only line ⊥ to �� WE at C true 

9. �FCE and �YCE are supplementary. true 

10. A�X� � X�C� true 

11. �FCD � �WBA false 

12. A�X� � F�C� false 

13. �� AB ⊥ A�C� false 

14. �XCF � �DCY true 

�� BM ⊥ �� MC , �� MA and �� MD are opposite rays. 

15. If m�DMC � 25, find m�AMB. 65 

16. If m�AMB � 72, find m�DMC. 18 

17. If m�DMC � 2x � 2 and m�AMB � 8x � 2, 

find m�DMC and m�AMB. 20; 70 


W 

A 

B 

C 

Z Y 

A 

X 

M 

D 

F 

B 

C 

D 

E

4–1 



Parallel Lines and Planes 

Describe each pair of segments in the prism as parallel, skew, or intersecting. 

1. E�G�, M�L� parallel 2. L�K�, E�G� skew 

3. L�K�, G�H� parallel 4. E�G�, G�H� intersecting 

5. J�N�, M�L� skew 6. L�K�, N�K� intersecting 

7. N�K�, J�H� parallel 8. E�G�, H�K� skew 

9. M�N�, L�K� parallel 10. M�N�, G�L� skew 

Use the figure for Exercises 1–10. Name the parts of the rectangular prism. 

11. six planes EGH, GLK, MLK, EMN, EMG, JNK 

12. all pairs of parallel planes EGH || MLK, MLG || NKH, EMN || GLK 

13. all segments skew to J�H� M�N�, L�K� 

14. all segments parallel to E�G� J�H�, M�L�, N�K� 

15. all segments intersecting M�L� IE�M�, M�N�, L�K�, GL 

16. all segments parallel to J�N� IH�K�, E�M�, G�L� 

Name the parts of the triangular prism. 

17. all pairs of intersecting planes BFD and BFY, BFD and FDZ, BFD and BDZ, 

XYZ and XZD, XYZ and XYF, XYZ and YZD 

18. all pairs of parallel segments F�D� || Y�Z�, 

B�X� || D�Z�, B�X� || F�Y�, D�Z� || F�Y�, B�D� || X�Z�, B�F� || X�Y� 

19. all pairs of skew segments B�F� and X�Z�, B�F� and Y�Z�, F�D� 

and X�Y�, F�D� and X�Z�, B�D� and X�Y�, B�D� and Y�Z�, F�Y� and X�Z�, F�Y� and B�D�, B�X� 

and F�D�, B�X� and Y�Z�, D�Z� and X�Y�, D�Z� and B�F� 

20. all points at which three segments intersect B, F, D, X, Y, Z 

J H 


B 

F 

M 

E G 

D 

N 

Y 

X 

K 

L 

Z

4–2 



Parallel Lines and Transversals 

Identify each pair of angles as alternate interior, 

alternate exterior, consecutive interior, or vertical. 

1. �1 and �6 2. �2 and �3 

vertical consecutive interior 

3. �2 and �7 4. �1 and �8 

alternate interior alternate exterior 

5. �2 and �5 6. �10 and �11 


7. �13 and �12 8. �5 and �4 

alternate exterior alternate exterior 

9. �3 and �8 10. �14 and �15 


11. �9 and �14 12. �14 and �11 

vertical alternate interior 

Find the measure of each angle. Give a reason for each answer. 

13. �7 45; 14. �4 45; 

Vertical angles Alternate 

are congruent. interior angles are 

congruent. 

15. �3 135; 16. �6 135; 

Consecutive interior Linear pairs are 

angles are 

supplementary. 


Find the measure of each angle. Give a reason for each answer. 

17. �1 125; Linear pairs are supplementary. 

18. �3 55; Vertical angles are congruent. 

19. �12 80; Consecutive interior angles are 


20. �11 100; Alternate interior angles are congruent. 

1 2 

5 6 3 4 

7 8 

13 14 15 16 

9 10 11 12 


1 

3 

2 

4 

55° 1 

2 3 

45° 

6 

5 

7 

10 8 

9 100° 

4 5 11 

12 

6 7 13 14

4–3 



Transversals and Corresponding Angles 

In the figure, m � p. Name all angles 

congruent to the given angle. Give a 

reason for each answer. 

1. �1 �6, vertical; 

�9, corresponding; 

�14, alternate exterior 

3. �13 �10, vertical; 



5. �9 �14, vertical; 

�6, alternate interior; 

�1, corresponding 

Find the measure of each numbered angle. 

7. 8. 

1 2 

3 4 

40° 

6 

5 7 

m�1 � 40, m�2 � 140, m�3 � m�1 � 35, m�2 � 80, m�3 � 

140, m�4 � 40, m�5 � 140, 80, m�4 � 100, m�5 � 65, 

m�6 � 140, m�7 � 40 m�6 � 65, m�7 � 65, m�8 � 

115, m�9 � 65, m�10 � 115, 

m�11 � 100, m�12 � 80 

9. 10. 

70° 6 5 4 

7 8 70° 3 

50° 

9 

1 10 11 12 

15 2 14 13 







6. �16 �11, vertical; 



14 13 

8 9 

78° 5 6 7 

1 2 3 4 

m�1 � 70, m�2 � 70, m�3 � m�1 � 102, m�2 � 78, m�3 � 

60, m�4 � 70, m�5 � 110, 102, m�4 � 78, m�5 � 102, 

m�6 � 110, m�7 � 110, m�8 m�6 � 78, m�7 � 102, m�8 � 

� 70, m�9 � 40, m�10 � 70, 102, m�9 � 78, m�10 � 102, 

m�11 � 60, m�12 � 120, m�13 � m�11 � 78, m�12 � 102, 

60, m�14 � 120, m�15 � 70 m�13 � 102, m�14 � 78 


35° 

5 80° 

2 6 

1 

4 3 7 8 

12 11 10 9 

12 

10 11 

1 2 

5 6 

9 10 

13 14 

3 4 

7 8 

11 12 

15 16 

m 

p

4–4 

Proving Lines Parallel 

Find x so that c � d. 

48 41c d 

23 

(4x � 3)° 

d 

12 c 

12 

55° 

135° 

13. b 

14. C 

D 

15. 

a 

95° 

75° 100° 

75° 

55° 

c 

d 

(2x � 8)° 

7. c 

8. c 

9. 

85° 



1. 2. 3. 

48° 

c 

4. 5. 6. 

d 

(9x � 4)° 

9 19 

Name the pairs of parallel lines or segments. 

10. 11. A B 

12. 

c � d 

x° d 

(3x � 8)° 

D 

82° 

d 

40° 75° 

C 

75° 

a � b A�B� � D�E� W�X� � Z�Y�, W�Z� � X�Y� 

C�D� � E�F� 

(7x � 2)° 


E 

85° 

F E 

c 

d 

(6x � 1)° c 

7 

14 

70° 

d 

70° 

110° 

(5x)° 

115° 

(5x � 11)° 

24° 

(6x � 6)° 

W X 

56° 

124° 

d 

c 

d 

124° 56° 

Z 

c 

d 

a 

b 

c 

a � b � c 

Y

4–5 

Slope 

Find the slope of each line. 



1. y 

2. y 

3. 

(�1, 1) 

O 

1 �2 undefined 

�� 4 

4. y 

5. y 

6. 

O 

(3, 2) 

(�2,�3) (2, �3) 

x 

0 �1 6 

7. y 

8. y 

9. 

(�1, 2) 

O 

(3, 0) 

x 

x 

(�1, 3) 

�� 1 

� undefined �1 

2 2 � 

Given each set of points, determine if �� AB and �� CD are parallel, perpendicular, or neither. 

10. A(1, 1), B(�2, 3), C(4, �1), D(6, 2) perpendicular 

11. A(0, 5), B(5, 0), C(3, 2), D(4, 1) parallel 

12. A(�2, 3), B(4, 5), C(0, 3), D(1, 0) perpendicular 

13. A(0, 0), B(4, 5), C(0, 3), D(5, �4) neither 

x 

(1, �1) 

14. A(�1, 1), B(3, �2), C(5, 0), D(3, �7) neither 

15. A(2, �5), B(5, �2), C(�3, 1), D(�4, 0) parallel 

16. A(2, �1), B(5, �3), C(�2, �2), D(3, 3) neither 

17. A(3, 0), B(6, �3), C(4, 3), D(5, 4) perpendicular 

O 

(�2, 4) (0, 2) 

O 

O 


(1, 3) 

(1, �2) 

x 

x 

O 

y 

(2,�2) 

O 

y 

(3, 4) 

y 

(2, 4) 

(�1, 1) (1, 2) 

O 

x 

x 

(2, �2) 

x

4–6 



Equations of Lines 

Name the slope and y-intercept of the graph of each equation. 

1. y � 3x � 2 3; 2 2. y ��4x � 1 �4; 1 

3. y � 2x � 5 2; 5 4. y ��5x � 1 �5; �1 

5. x � 2 undefined; none 6. 10x � y � 7 �10; 7 

7. y � 3x ��1 �3; �1 8. y � x 1;0 

9. 2x � y � 3 2; �3 10. y ��6 0; �6 

11. �4x � y � 8 �4; �8 12. 2x � 2y � 14 �1; 7 

13. 9x � 3y � 12 3; �4 14. 5x � 10y � 20 

1 

� ;2 

Graph each equation using the slope and y-intercept. 

15. y � 2x � 1 16. y � x � 3 

17. x � y � �4 18. 3x � y � 2 

O 

y 

y � 2x � 1 

O 

x 

y 

19. 2x � y ��1 20. �3x � y � 2 

y 

x � y � 4 

x 

2x � y � �1 

O 

x 


O 

O 

O 

y 

y � x � 3 

y 

y 

�3x � y � 2 

� 2 

x 

3x � y � 2 

x 

x

5–1 



Classifying Triangles 

Classify each triangle by its angles and by its sides. 

1. 6 in. 

2. 3. 

6 in. 

60° 

60° 

60° 

6 in. 

acute, equilateral right, scalene isosceles, obtuse 

4. 15 m 

5. 6. 

50° 50° 

11 m 11 m 

80° 

isosceles, acute scalene, obtuse isosceles, acute 

7. 8. 9. 

32° 

obtuse, scalene acute, equilateral isosceles, right 

Make a sketch of each triangle. If it is not possible to sketch the 

figure, write not possible. 

10. right scalene 11. obtuse isosceles 

12. right isosceles 13. right equilateral 

not possible 

3 cm 

20 cm 

55° 

100° 

22 cm 

35° 

4 cm 

38° 

42° 

60° 


5 cm 

30 cm 

130° 18° 60° 

60° 

16 ft 

100° 

16 ft 

40° 40° 

25 ft 

45° 

72° 72° 

36° 

45°

5–2 

Angles of a Triangle 

Find the value of each variable. 



1. 2. 3. 

x° 

55° 

35 40 35 

4. 5. 6. 

50° 45° 

85 38 52 

7. 18° 

8. 9. 

72 45 45 

10. 11. 12. 

x° 

x° 

50° 

40 42 105 

Find the measure of each angle in each triangle. 

13. 43° x° 

14. 

64° 

x° 

73 32, 58 

70° 

x° 


70° 

x° 52° 

135° 

110° 

x° x° 

44° 

x° 60° 

x° 

x° 45° 

48° 

(3x � 10)° 

(2x)° 

75° x° 

84° 

30° 

x°

5–3 



Geometry in Motion 

Identify each motion as a translation, reflection, or rotation. 

1. 2. 3. 

translation rotation translation 

4. 5. 6. 

reflection translation rotation 

7. 8. 9. 

reflection translation rotation 

In the figure at the right, quadrilateral 

ABCD → quadrilateral WXYZ. 

10. Which angle corresponds to �D? �Z 

11. Which side corresponds to X�Y�? B�C� 

12. Name the image of point A. point W 

13. Name the image of A�D�. W�Z� 

14. Which vertex of ABCD corresponds to Y? C 

15. Name the side that corresponds to A�B�. W�X� 


A 

W 

B 

C 

X 

Z 

Y 

D

5–4 



Congruent Triangles 

Name the congruent angles and sides for each pair of congruent triangles. Then draw 

arcs and slash marks to show the congruent angles and sides. 

1. 2. 

A X 

C 

�ACE � �XYZ �MNO � �CBA 

�A � �X, �C � �Y, �E � �Z, �M � �C, �N � �B, �O � �A, 

A�C� � X�Y�, C�E� � Y�Z�, A�E� � X�Z� M�N� � C�B�, N�O� � B�A�, M�O� � C�A� 

3. N 

4. 

D 

E 

B Z 

B 

Z Q 

�BDE � �ZNQ �TRI � �ZAC 

�B � �Z, �D � �N, �E � �Q, �T � �Z, �R � �A, �I � �C, 

B�D� � Z�N�,D�E� � N�Q�,B�E� � Z�Q� T�R� � Z�A�,R�I� � A�C�,T�I� � Z�C� 

Complete each congruence statement. 

5. C 

B 

6. 

A X R 

�CAX � � ? BRX �ZWO � � ? ARO 

7. 8. 

A 

B 

D 

�MAB � � ? MCD �EIX � � ? OIY 

9. 10. 

Y 

M 

C 

E 

A B 

L 

D C 

X Y 

�ABD � � ? CDB �LMO � � ? CBA 


T 

R 

O 

Z 

A 

M 

Z 

I 

O 

I 

A 

O N 

R 

M 

A 

C 

W 

C 

C 

A 

O 

B 

B

5–5 



SSS and SAS 

Write a congruence statement for each pair of triangles represented. 

1. A�C� � N�O�, C�L� � O�P�, �C � �O 2. W�X� � A�B�, X�Z� � B�C�, W�Z� � A�C� 

�ACL � �NOP �WXZ � �ABC 

3. E�G� � P�S�, E�H� � P�T�, �E � �P 4. H�Y� � R�P�, E�Y� � A�P�, �Y � �P 

�EGH � �PST �HEY � �RAP 

5. Z�A� � Q�R�, A�P� � R�S�, Z�P� � Q�S� 6. M�L� � Z�N�, L�R� � N�B�, �L � �N 

�ZAP � �QRS �MRL � �ZBN 

Determine whether each pair of triangles is congruent. If so, write a congruence 

statement and explain why the triangles are congruent. 

7. A B C 

8. 

�ABD � �CBD; SAS �AER � �WDG; SSS 

9. 10. 

G 

D 

H I D 

E 

J 

�HGE � �HIJ; SAS �QAD � �QAU; SAS 

11. P 

12. 

L R 

�PLR � �RAP; SSS �UWZ � �XWY; SAS 

Use the given information to determine whether the two triangles are congruent by 

SAS. Write yes or no. 

13. � L � � M, L�D� � M�R�, L�O� � M�A� yes 

14. � L � � M, L�D� � M�R�, � O � � A, no 

15. L�D� � M�R�, L�O� � M�A�, � O � � A, no 

16. L�D� � M�R�, L�O� � M�A�, � D�O� � R�A� no 

A 


A 

A 

U 

U 

Z 

R 

D 

E 

G 

W 

W 

L 

Q 

X 

Y 

D 

R 

O 

M 

A

5–6 



ASA and AAS 

Write a congruence statement for each pair of triangles represented. 

1. In �ABC and �ZXR, �C � �X, �A � �Z, and A�B� � Z�R�. �ABC � �ZRX 

2. In �DEF and �BGO, �D � �B, �E � �O, and D�E� � B�O�. �DEF � �BOG 

3. In �TRI and �GAN, �T � �A, T�I� � A�G�, and T�R� � A�N�. �TRI � �ANG 

4. In �ZIP and �LOS, �P � �O, �I � �L, and P�I� � O�L�. �ZIP � �SLO 

Name the additional congruent parts needed so that the triangles are congruent by 

the postulate or theorem indicated. 

5. AAS 6. ASA 

M 

�R � �D �S � �B 

7. AAS 8. ASA 

O 

O�N� � A�C� or M�O� � B�A� X�Z� � B�C� 

Determine whether each pair of triangles is congruent by SSS, SAS, ASA, or AAS. If it 

is not possible to prove that they are congruent, write not possible. 

9. F 

10. 

I 

F 

R D 

A 

C 

SSS ASA 

11. 12. 

A 

M B 

N 

B 

H 

N 

C 

C 

A 

G 

V 

K 

not possible AAS 

S T 


A 

X 

X 

C 

Z 

V 

Y 

S 

C 

A 

R 

B 

B 

T 

R

6–1 

Medians 



A�D�, B�E�, and C�F� are medians of �ACE. 

1. If AE � 24, find AF. 12 

2. Find AE, if FE � 15. 30 

3. What is BC if AC � 36? 18 

4. Find CE, if DE � 7. 14 

5. What is CD if CE � 68? 34 

6. If AF � 3, find AE. 6 

T�R�, Z�X�, and S�W� are medians of �TXS. 

7. If TX � 18, find TW. 9 

8. If TO � 26, find OR. 13 

9. If WO � 5, find OS. 10 

10. Find ZO if OX � 50. 25 

11. What is TZ if TS is 2? 1 

12. What is OS if OW is 9? 18 

R�N�, P�M�, and L�O� are medians of �LNP. 

13. What is LP if RL is 4? 8 

14. Find AO if LO � 18 6 

15. What is RA if AN is 42? 21 

16. If MA � 13, find MP. 39 

17. Find AN if RN � 30. 20 

18. If LO � 15, find AO. 5 


A 

S 

P 

Z 

R 

F 

B 

T 

O 

L 

A 

O 

M 

R 

E 

M 

D 

W 

C 

N 

X

6–2 



Altitudes and Perpendicular Bisectors 

Tell whether the bold segment or line is an altitude, a perpendicular bisector, both, or 

neither. 

1. 2. 3. 

both neither altitude 

4. 5. 6. 

neither both perpendicular 

bisector 

7. 8. 9. 

both altitude perpendicular 

bisector 

10. 11. 12. 

neither perpendicular both 

bisector 


13. Name a segment in the triangle that is an 

altitude. A�C� or B�C� 

14. Name a segment in the triangle that is a 

perpendicular bisector. F�D� 

14. Name a segment in the triangle that is not 

an altitude and is not a perpendicular 

bisector. A�G� 


A 

D 

E 

C 

F G 

B

6–3 



Angle Bisectors of Triangles 

In �ACD, D�B�� bisects �ADC, and C�E�� bisects �ACD. 

1. If m�1 � 40, what is m�2? 40 

2. Find m�ACD if m�4 � 25. 50 

3. What is m�3 if m�ACD � 36? 18 

4. If m�1 � 45, what is m�ADC? 90 

5. What is m�DCA if m�DCE � 20? 40 

6. Find m�ADB if m�BDC � 39. 39 

7. What is m�ACD if m�4 � 18? 36 

8. Find m�2 if m�1 � 43. 43 

9. If m�3 � 21, what is m�4? 21 

10. What is m�ECD if m�ECA � 24? 24 

In �MOR, M�P� bisects �OMR, R�N� bisects �MRO, and O�S� bisects �MOR. 

11. Find m�6 if m�MOR � 34. 17 

12. What is m�OMR if m�1 � 23? 46 

13. If m�3 � 55, what is m�4? 55 

14. What is m�MOS if m�MOR � 32? 16 

15. Find m�1 if m�2 � 27. 27 

16. If m�4 � 60, what is m�MRO? 120 

17. What is m�SOR if m�6 � 15? 15 

18. If m�MRP � 112, what is m�3? 56 

19. Find m�OMP if m�PMR � 30. 30 

20. What is m�4 if �MRO is a right angle? 45 


M 

D 

E 

1 2 

2 1 

S 

A 

N 

3 4 

R 

B 

3 4 

6 

5 

P 

C 

O

6–4 

Isosceles Triangles 



Find the values of the variables for each triangle. 

1. A 

2. D 

3. X Z 

10 

a° 

b 

F 

40° 

y° 

x° 

E 

Y 

54° c° 

C 

60° 60° 

B 

d° 

A 

B 

a � 60; b � 10 x � 40; y � 100 c � 54; d � 63 

4. B 

5. C 

6. 

x° 

y 

4 45° 

W O 

x � 45; y � 4 a � 60; b � 68 x � 70; y � 110 

7. W X 

8. S 

9. 

b° a° 

R 60° 

Y 

24° 

a � 102; b � 78 x � 90; y � 60 a � 60; b � 64 

10. 11. 12. 

a � 45; x � 90 c � 92; d � 44 a � 46; b � 96 


13. In �ADF, if AD � x � 6 and DF � 3x � 10, 

what is AD? 14 

14. In �ADH, if m�ADH � 2x � 4, find the 

value of x. 24 

P 60° a° A 

b° 

x° 

A 

x° a° d° 

15. If AH � 5x � 1 and FH � 3x � 21, what is 

AH? 54 

16. In �ADF, what is m�ADF? 88 

y° 

44° 

M 

45° 

c° 

44° 


T 

D 

R 

40° 

x° y° 

C A 

a° 

E 

42° 

Z 

b° 

b° 

46° 

A H F 

D 

a° 

88° 

B 

52°

6–5 

Right Triangles 


Determine whether each pair of right triangles is congruent by LL, HA, LA, or HL. If it is not 

possible to prove that they are conguent, write not possible. 

1. 2. 

M E F 

W X Y 

D A 

G 

LL HL 

3. 4. 

A C 

R 

D E 

M 

not possible HA 

5. 6. 

Q 

R 

T 

S 

HL LL 

7. 8. 

R 

T S 

HL HA 

9. 10. 

C 

F 

D I G 


LA not possible 


V 

T 

A B 

C 

E 

M 

P 

A B 

Z 

A 

S C B 

A 

D 

E D C 

R 

Q

6–6 


The Pythagorean Theorem 

Find the missing measure in each right triangle. Round to the nearest tenth, if necessary. 

1. 2. c in. 

3. 

4 cm 

3 cm 

c cm 

10 in. 

5 26.9 26.2 

4. 8 in. 

5. 6. 

b in. 

9 in. 

4.1 26.2 3.4 

7. 8. 25 m 

9. 

3 in. 

5 in. 

c in. 


a m 

5.8 14.7 23.2 

29 m 

Find each missing measure if c is the measure of the hypotenuse. Round to the 

nearest tenth, if necessary. 

10. a � 15, b � 10, c � ? 18.0 

11. b � 6, c � 10, a � ? 8 

12. c � 100, b � 60, a � ? 80 

13. c � 16, a � 9, b � ? 13.2 

14. a � 2, b � 3, c � ? 3.6 

15. c � 5, b � 2, a � ? 4.6 

16. b � 7, c � 15, a � ? 13.3 

17. c � 30, a � 20, b � ? 22.4 

The lengths of three sides of a triangle are given. Determine whether each triangle is 

a right triangle. 

18. 3 cm, 4 cm, 5 cm yes 

19. 1 ft, 1 ft, 2 ft no 

20. 2 in., 2 in., 4 in. no 

21. 8 m, 15 m, 17 m yes 

22. 5 in., 10 in., 15 in. no 

23. 14 cm, 48 cm, 50 cm yes 

10 m 


25 in. 

28 m 

a m 

20 ft 

4.5 m 

a m 

b ft 

24 ft 

33 ft 

3 m 

b ft 

6 ft

6–7 NAME DATE PERIOD 


Distance on the Coordinate Plane 

Find the distance between each pair of points. Round to the nearest tenth, if necessary. 

1. X(4, 0), Y(2, 0) 2 2. C(–3, 0), D(–8, 0) 5 

3. F(5, 0), G(–1, 0) 6 4. F(0, 8), G(0, 1) 7 

5. M(0, –1), N(0, –6) 5 6. R(0, 6), S(0, –2) 8 

7. A(2, –1), B(5, 3) 5 8. D(1, –5), E(1, 5) 10 

9. H(–3, 4), I(5, 4) 8 10. G(0, 0), H(6, 8) 10 

11. K(0, 0), M(–3, –4) 5 12. A(0, 7), C(24, 0) 25 

13. E(1, 1), A(–1, –1) 2.8 14. M(0, 4), Z(–2, 5) 2.2 

15. A(–1, –2), Z(2, 1) 4.2 16. Y(5, 6), B(–5, –6) 15.6 

17. C(2, –3), X(2, 7) 10 18. D(6, 9), U(9, 6) 4.2 

19. L(5, 3), M(–1, 0) 6.7 20. S(–2, –6), T(7, 6) 15 

21. H(1, –1), A(–5, 4) 7.8 22. G(8, –9), X(–1, 0) 12.7 

23. B(–7, 4), T(–10, –1) 5.8 24. W(4, –2), N(1, 2) 5 


7–1 



Segments, Angles, and Inequalities 

For Exercises 1–12, use the figure below. 

A B C D O E F G H 

�20 �15 �10 �5 0 5 10 15 20 

Replace each � with �, �, or� to make a true sentence. 

1. AB � FH � 2. AD � EH � 3. AE � HE � 

4. AE � DE � 5. DF � OG � 6. CG � BF � 

Determine whether each statement is true or false. 

7. AF � BG true 8. OE � DF true 9. CG � OH false 

10. BD � FG true 11. OH � OA true 12. AG � BH true 

For Exercises 13–24, use the figure at the right. 

Lines AJ, DM, and GO intersect at P. 

Replace each � with �, �, or�to make a true sentence. 

13. m�APD � m�MPJ � 14. m�DPG � m�APD � 

15. m�DPG � m�GPJ � 16. m�APO � m�GPJ � 

17. m�MPJ � m�OPM � 18. m�APO � m�DPG � 

Determine if each statement is true or false. 

19. m�OPJ � m�APG true 20. m�OPJ � m�GPJ false 

21. m�OPJ � m�DPG true 22. m�APG � m�GPJ false 

23. m�DPJ � m�APM false 24. m�APO � 2 • m�APD false 


A 

O 

D 

45° 

55° 

P 

M 

G 

J

7–2 

Exterior Angle Theorem 

Name the angles. 



1. an exterior angle of �ABX 2. an exterior angle of �BEA 

�7 or �9 �5 

3. an interior angle of �ABX 4. an interior angle of �BEA 

�1, �6, or �ABX �1, �2, or �3 

5. a remote interior angle of 6. a remote interior angle of 

�ABX with respect to �7 �BEA with respect to �5 

�1 or �ABX �1 or �2 

Find the measure of each angle. 

7. �C 32 8. �1 40 9. �2 122 

10. �3 148 11. �4 115 12. �5 55 

M 

3 

B 

58° 

A D C 

A 

93° 55° 


13. Find the value of x. 50 

R 

14. Find m�B. 50 

15. Find m�BMA. 105 

16. Find m�BMZ. 75 

Replace each � with �, �, or� to make a true sentence. 

17. 18. 19. 

A B 

1 

2 

4 

C 

3 

Y 

E 

4 

3 

68° 

A 

E 

1 

X 

1 

105° 65° 

Z Y 

2 

47° 

X 

m�3 � m�1 � m�5 � m�3 � m�2 � m�4 � m�6 � 


G 

4 5 6 

G 

A 

R 

72° 

1 

50° 

U 

R T 

135° 

5 

F 

1 

J 2 

3 

I 

4 

T 

2 

80° 

W 

B 

2 4 

X 

35 67 C 

E 98 

D 

B 

x° 

(2x � 5)° 

55° 

A M Z 

5 

6 

H

7–3 



Inequalities Within a Triangle 

List the angles in order from least to greatest measure. 

1. A 

2. W 

3. 

3 in. 

D 

5 in. 

18 cm 

4 in. C 

Z 

30 cm X 

�C, �A, �D �X, �Z, �W O �O, �A, �M 

4. B 

5. R 

6. 

C 

A 

�B, �C, �A �R, �O, �Z �X, �Y, �V 

List the sides in order from least to greatest measure. 

7. C 

8. R 

9. 

B 

27 m 

18 m 

24 m 

T 

A�B�, B�C�, A�C� A�T�, R�T�, R�A� M�Y�, Y�L�, M�L� 

Identify the angle with the greatest measure. 

10. 12 in. 

11. D 

12. 

A 

70° 

50° 

60° 

A 

�B �F 

70° 

A 

Identify the side with the greatest measure. 

13. J 

14. M 

15. 

L 

14 in. 

55° 

C 

53° 

B 

11 in. 

10 cm 

L�J� M�N� P�Q� 

Z 

11 cm 

8 cm 

35° 

75° 

16 cm 


O 

26 cm 

95° 37° 

72° O 

K 

F 

48° 

17 cm 

13 cm 

E 

N 

Y 

M 

Y 

M 

4 ft 

62° 

6 ft 

A 

V 

8 ft 

9 in. 13 in. 

19 mm 

I 

27 mm 

R 

61° 

16 in. 

G 

P 

59° 

28° 

38 mm 

H 

60° 

L 

Q 

X 

�I

7–4 



Triangle Inequality Theorem 

Determine if the three numbers can be measures of the sides of a triangle. Write yes 

or no. Explain. 

1. 6, 7, 8 yes; 2. 1, 1, 2 no; 3. 2, 4, 6 no; 

6 � 7 � 8, 1 � 1 � 2 2� 4 � 6 

7 � 8 � 6, 

6 � 8 � 7 

4. 5, 8, 10 yes; 5. 10, 20, 30 no; 6. 3, 4, 5 yes; 

5 � 8 � 10, 10 � 20 � 30 3 � 4 � 5, 

8 � 10 � 5, 4 � 5 � 3, 

5 � 10 � 8 3 � 5 � 4 

7. 3, 5, 7 yes; 8. 6, 12, 24 no; 9. 1, 7, 10 no; 

3 � 5 � 7, 6 � 12 � 24 1 � 7 � 10 

5 � 7 � 3, 

3 � 7 � 5 

10. 10, 15, 26 no; 11. 8, 12, 19 yes; 12. 4, 7, 10 yes; 

10 � 15 � 26 8 � 12 � 19, 4 � 7 � 10, 

12 � 19 � 8, 7 � 10 � 4, 

8 � 19 � 12 4 � 10 � 7 

Find the range of possible measures for the third side of a triangle with the measures 

given for two sides. 

13. 7, 13 6 � x � 20 14. 20, 25 5 � x � 45 15. 1, 5 4 � x � 6 

16. 32, 38 6 � x � 70 17. 50 ,70 20 � x � 120 18. 8, 20 12 � x � 28 

19. 55, 10 45 � x � 65 20. 2, 10 8 � x � 12 21. 60, 70 10 � x � 130 

22. 45, 70 25 � x � 115 23. 9, 19 10 � x � 28 24. 100, 120 20 � x � 220 


8–1 

Quadrilaterals 



Refer to quadrilaterals ABCD and MNOZ. 

1. Name the side opposite B�C�. A�D� 

2. Name a side that is consecutive with A�B�. 

B�C� or A�D� 

3. Name a pair of consecutive vertices in ABCD. 

A and B or B and C or C and D or A and D 

4. Name the vertex opposite B. D 

5. Name the two diagonals in ABCD. A�C� and B�D� 

6. Name a pair of consecutive angles in MNOZ. 

Sample answer: �M and �N 

7. Name the vertex opposite O. M 

8. Name the side opposite M�Z�. N�O� 

9. Name a side that is consecutive with M�N�. 

N�O� or M�Z� 

10. Name the diagonals in MNOZ. M�O� and N�Z� 

Find the missing measure(s) in each figure. 

11. 12. 

110° 

70° 

105 98 

13. 14. 

x° 

x° 

75° 

110° 

130° 80° 

40 90, 90, 90, 90 

15. 16. 

60, 120, 60, 120 130, 130 


72° 

x° 

120° 

Z 

D 

x° 

x° x° 

A 

C 

Exercises 1 - 5 

M N 

B 


x° 2x° 

x° 

50° 

2x° 

x° 

50° 

x° 

70° 

x° 

O

8–2 

Parallelograms 



Find each measure. 

1. m�H 130 2. m�G 50 

3. GH 25 4. FG 40 


5. m�Z 60 6. m�W 120 

7. XY 7 8. WX 7 

In the figure, TQ � 42 and SA � 14. Find each measure. 

9. TA 21 10. m�QST 110 

11. SR 28 12. m�STR 70 

13. SQ 22 14. ST 30 

15. AQ 21 16. AR 14 

17. In a parallelogram, the measure of one side is 38. Find the measure of 

the opposite side. 38 

18. The measure of one angle of a parallelogram is 45. Determine the 

measures of the other three angles. 45, 135, 135 


I 

25 

50° 

Q 

Z 

F G 

40 

7 

H 

W X 

120° 

7 Y 

S T 

30 

A 

45° 65° 

R 

22

8–3 



Tests for Parallelograms 

Determine whether each quadrilateral is a parallelogram. Write yes or no. If yes, 

give a reason for your answer. 

1. 2. 3. 

yes, Theorem 8-7 yes, Theorem 8-9 yes, definition 

of parallelogram 

4. 5. 6. 

no yes, definition no 


7. 8. 9. 

yes, Theorem 8-8 yes, Theorem 8-9 no 

10. 11. 12. 

70° 

110° 

110° 

70° 

50° 

130° 

yes, definition no yes, Theorem 8-8 



105° 

75° 

90° 90°

8–4 



Rectangles, Rhombi, and Squares 

Identify each parallelogram as a rectangle, rhombus, square, or none of these. 

1. 2. 3. 

none of these square rhombus 

4. 5. 6. 

none of these rectangle none of these 


7. BO 10 8. OC 10 

9. AC 20 10. BD 20 

11. m�AOB 90 12. m�ABC 90 

13. m�ADB 45 14. m�DCA 45 

15. MG 18 16. HF 20 

17. m�EHG 120 18. m�FEH 60 

19. m�EMF 90 20. FG 22 

21. EF 22 22. m�FGE 30 

10 cm O 


E 

A 

D 

B 

C 


18 in. 

M 

60° 10 in. 

H 

F 

22 in. 


G

8–5 

Trapezoids 



For each trapezoid, name the bases, the legs, and the base angles. 

1. 2. 3. 

G 

Find the length of the median in each trapezoid. 

4. 3 ft 

5. 6. 

5 ft 

A 

C 

A�C�,� G�E�; A�G�, C�E�; �A 

and �C, �G and �E 

E 

W�Z�, X�Y�;W�X�, Z�Y�; �W 

and �Z, �X and �Y 

17 cm 

7. 14 yd 8. 7 in. 

9. 

15 m 

26 yd 4 in. 8.5 m 

Find the missing angle measures in each isosceles trapezoid. 

10. 11. N 

12. 

D 

55° 

55, 125, 125 124, 56, 56 105, 75, 75 

13. H B 14. D M 15. 

64° 

F 

7 ft 

38 yd 

A B 

D 

C 

X 

W 

Z 

10 cm 

M 

124° 

P 

O 

T�R�, P�A�;T�P�, A�R�; �T 

and �R, �P and �A 

64, 116, 116 150, 30, 30 72, 108, 108 

X 

Y 

1 in. 

T R 


24 cm 

150° 

O 

P 

16 m 

14 m 

5 m 

105° 

D 

12 m 

A 

Q U 

T 

72° 

A 

C A 

X

9–1 



Using Ratios and Proportions 

Write each ratio in simplest form. 

1. 

15 

� 

20 

3 

� 

4 

2. 

7 

� 

49 

1 

� 

7 

3. 

28 4 

11 1 

4. � � 5. � � 6. 

35 5 

22 2 

3 1 

18 2 

7. � � 8. � � 9. 

15 5 

81 9 

55 5 

12 6 

10. � � 11. � � or 6 12. 

33 3 

2 1 

3 

13. 15 feet to 25 feet � 14. 48 centimeters to 15 centimeters 

5 

3 

15. 45 meters to 60 meters � 16. 14 inches to 24 inches 

4 

1 

17. 12 inches to 3 feet � 18. 80 centimeters to 2 meters 

3 

2 

19. 4 feet to 10 yards � 20. 8 quarts to 5 gallons 

15 

Solve each proportion. 

3 6 

24 x 

7 14 

21. � � � 16 22. � � � 4 23. � � � 24 

8 x 

18 3 

12 x 

8 x 

4 x 

32 16 

24. � � � 6 25. � � � 6 26. � � � 3 

28 21 

8 12 

6 x 

9 x 

5 35 

22 x 

27. � � � 36 28. � � � 10 29. � � � 33 

5 20 

x 70 

18 27 

2 14 

8 56 

x 6 

30. � � � 3 31. � � � 1 32. � � � 1 

x 21 

x 7 

5 30 


10 

� 15 

20 

� 25 

36 

� 27 

40 

� 25 

2 

� 5 

2 

� 3 

4 

� 5 

4 

� 3 

8 

� 5 

7 

� 12 

2 

� 5 

16 

� 5

9–2 

Similar Polygons 


Determine whether each pair of polygons is similar. Justify your answer. 

1. 3 

6 2. 2 5 

3. 

4 

3 

4 

8 

Yes; corresponding 

angles are congruent 

3 4 

and � � � . 

6 8 



and � . 

2 2 

� � 

5 5 

4. 3 

4 

5. 6. 

3 

3 

No; corresponding 

angles are not 

congruent. 

6 

8 



14 14 14 

and � � � � �. 26 26 26 

If each pair of polygons is similar, find the values of x and y. 

7. 8. 20 

9. 

y x 

20 

3 

6 12 

4 

4 

4 

10. 11. 12. 

11 

2 

2 

No; � . 

2 1 

� � 

3 5 



6 

and � is the ratio for 

10 

the lengths of all six 

sides. 

x � 8, y � 10 x � 30, y � 30 x � 6, y � 24 

3 

4 4 

10 

x 

16 

6 y 


14 

20 

14 

4 

4 

4 

4 

20 

4 

4 

x � 8, y � 20 x � 11, y � 11 x � 15, y � 24 

2 

5 

14 


20 

26 

5 

30 

y 

26 

x 

x 

y 

5 

26 

1 

6 

2 

1 

2 3 

6 

6 10 

6 6 10 

6 

4 

10 

6 

16 

16 

14 

9 

5 

5 

10 

10 

x 

10 

10 

6 

x 

y 

y 

3

9–3 

Similar Triangles 



Determine whether each pair of triangles is similar. If so, tell which similarity test is 

used and complete the statement. 

1. 2. 3. 

A 

�ABC � � ? 

yes; ZYM; SAS 

4. 5. 6. 

F 

�DEF � � ? 

not similar 

Find the value of each variable. 

�MNO � � ? 

yes; YBA; SSS 

�DYA � � ? 

yes; RMZ; AA 

7. 8. 9. 

14 

6 

10 

Z 

12 

C B 

20 

M Y 

10. 11. 12. 

4 

5 

O 3 N 

�BAC � � ? 

yes; ZYR; AA 

�FGI � � ? 

not similar 

x � 8 x � 16, y � 24 x � 3, y � 7 

8 

20 

7 

24 

D 

16 

24 

x 

Q 

7 

5 

12 

y 

D 

x 

E 

A 

M 

Y 

24 

24 

D 

B 

A 

24 

10 

R 

36 

36 

15 30 

x � 6, y � 18 x � 16, y � 24 x � 20, y � 28 

6 


A 

Y 

M 

y 

8 

16 

x 

y 

Z 

x 

A 

Z 

B C 

I 

30 

20 42 

x 

3 

R 

G 

Y 

F R 

y 

5 

7 

30 20 

y 

4 

D M 

x

9–4 

Complete each proportion. 


MB MD 

MR MW 

1. � = � DC 2. � = � WT 

BA ? 

RS ? 

BD MD 

MB ? 

3. � = � MC 4. � = � MD 

AC ? 

MA MC 

CD AB 

MS MT 

5. � = � BM 6. � = � MW 

DM ? 

RM ? 

ST SM 

MW ? 

7. � = � RM 8. � = � MR 

RW ? 

WT RS 

RW MW 

TW SR 

9. � = � MT 10. � = � RM 

ST ? 

WM ? 

CM ? 

SM TM 

11. � = � AM 12. � = � TW 

MD BM 

SR ? 

Find the value of x. 

13. 14. 15. 

12 

8 

C D 

10 6 25 

16. 17. 15 

18. 

24 7 9 

19. 5 

20. 21. 

10 

15 

25 

x 

15 x 

x 

2x 5 


Proportional Parts and Triangles 

15 

5 4 7.2 


42 

30 

15 x 18 

x 

7 

8 

20 

x 

15 

x 

18 

12 

x � 8 

A 

B 

9 

12 

x 

30 

M 

50 

36 

R 

21 

S 

W T

9–5 


In each figure, determine whether A�B� || R�S� . 

1. 2. 3. 

A 

15 

13 

R S 

30 

26 

yes yes no 

4. 5. 6. 

no no yes 

M, O, and R are the midpoints of the sides of �ABC. 

Complete each statement. 

C 

C 13 

7 

R 

S 23 

14 

A 

B 

7. O�R� | ? A�B� 

8. B�C� | ? �M�R� 

9. If MO � 15, then AC � ? 30 

10. If BC � 62, then MR � ? 31 

11. If m�BMO � 75, then m�BAC � ? 75 

12. If m�BCA � 52, then m�BOM � ? 52 

13. A�C� | ? M�O� 


Triangles and Parallel Lines 

14. If BM � 28, then AM � ? 28 

15. If AB � 50, then OR � ? 25 

16. If BC � 74, then BO � ? 37 

17. If m�COR � 60, then m�CBA � ? 60 

18. If BO � 19, then MR � ? 19 

A 8 

R 

32 

B 6 S 24 

C 

B 5 

R 7 

18 S 

A 


21 

C 

B 

M 

B 

R 

8 

C 

9 

S 

20 21 

A B 

A 

4 

R 

12 

C 

24 S 8 B 

O 

A R C

9–6 


Complete each proportion. 

1. 

TX 

� � 

XZ 

? 

� 

YA 

WY 

WY TX 

2. � � � 

WA ? 

TZ 

T 

YA XZ 

WA TZ 

3. � � � TX 4. � � � WY 

WY ? 

? TX 

AY XZ 

TZ WA 

5. � � � WY 6. � � � TX 

? TX 

? WY 

Find the value of x. 

7. 8. 9. 

10 

15 

15 20 18 

10. 11. 12. 

8 

8 

26 60 20 

13. 14. 15. 

9 

3 

x 

18 

5 

x 


Proportional Parts and Parallel Lines 

10 

x 

20 22 20 

30 

30 

20 

60 

9 

15 


x 

12 

x 

30 

88 

x 

X 

W 

Y 

Z A 

x 

12 10 

5 

7 

4 16 

5 

x 

x 

21 

15

9–7 


Find the value of each variable for each pair of similar triangles. 

1. A 

2. A 

3. 

18 

15 

C 12 B 

T 

R 

z y 

x 

S 

Perimeter of �RST � 30 Perimeter of �ADE � 24 Perimeter of �OPS � 9 

x � 8, y � 10, z � 12 x � 6, y � 8, z � 10 x � 3, y � 3, z � 3 

4. 5. 6. 

Perimeter of �MNO � 11 Perimeter of �DEF � 51 Perimeter of �QPZ � 168 

x � 5, y � 3, z � 3 x � 16, y � 12, z � 23 x � 49, y � 49, z � 70 

Determine the scale factor for each pair of similar triangles. 

Z 

18 

C 

15 

15 

X 

A 

B 

38 

25 

30 


Perimeters and Similarity 

M 

x N 

O 

y 

z 

A 

M 

9 

Y 

19 

15 

B 

2 

3 

7. �XYZ to �MBA � 8. �ADX to �MYB � 9. �FHA to �BLN 

1 

1 

1 

1 

10. �MBA to �XYZ � 11. �MYB to �ADX � 12. �BLN to �FHA 

2 

3 

13. The perimeter of �BDE is 72 feet. If �BDE � �FMR and the scale factor of 

4 

�BDE to �FMR is , find the perimeter of �FMR. 90 ft 

� 5 

A 

A 

M 

3 

N 

18 

5 

4 

32 

46 

27 

x 

P 


E 

X 

C 

15 

24 

z 

y 

B 

D x 

D 

M 

z 

D 

Y 

9 

5 

6 B 

F 

y 

E 

A 

H 

14 

R 

10 

20 

T 14 S 

28 

24 

N 

F 

10 

F 

x 

Z 

Q 

12 

H 

10 

42 

36 

G 

y 

z 

O 

x y 

S z P 

L 

B 

2 

� 3 

3 

� 2 

P 

18

10–1 

Naming Polygons 

Identify each polygon by its sides. Then determine whether it appears to be regular or not 

regular. If not regular, explain why. 

1. 2. 3. 

quadrilateral, not triangle, regular quadrilateral, not 

regular; sides are not regular; sides not 

all congruent congruent, angles 

not congruent 

Name each part of hexagon ABCDEF. 

4. two consecutive vertices 

Sample answer: A, B 

NAME ______________________________________DATE __________PERIOD______ 


5. two diagonals 

Sample answer: A�C�, A�D� 

6. all nonconsecutive sides of A�B� 

Sample answer: C�D�, D�E�, E�F� 

7. any three consecutive sides 

Sample answer: A�B�, B�C�, C�D� 

8. any four consecutive vertices 

Sample answer: A, B, C, D 

E D 

Classify each polygon as convex or concave. 

9. 10. 11. 

convex convex concave 

12. 13. 14. 

concave convex concave 


F 

A 

B 

C

10–2 



Diagonals and Angle Measure 

Find the sum of the measures of the interior angles in each figure. 

1. X 

2. A B 

3. 

180 720 360 

4. E 

5. I 

6. 

H 

J 

R 

Z 

Z 

L 

M 

Y 

F 

P 

540 1260 180 

O 

E 

N 

Find the measure of one interior angle and one exterior angle of each regular polygon. If 

necessary, round to the nearest degree. 

7. triangle 8. octagon 9. decagon 

60, 120 135, 45 144, 36 

10. nonagon 11. quadrilateral 12. hexagon 

140, 40 90, 90 120, 60 

13. The sum of the measures of three interior angles of a quadrilateral is 245. What is the 

measure of the fourth interior angle? 115 

14. The sum of the measures of six exterior angles of a heptagon is 310. What is the measure 

of the seventh exterior angle? 50 

15. The sum of the measures of seven interior angles of an octagon is 1000. What is the 

measure of the eighth interior angle? 80 

16. The sum of the measures of nine exterior angles of a decagon is 325. What is the measure 

of the tenth exterior angle? 35 


M 

D 

L 

C 

K 

T 

D 

L 

Q 

S 

A 

R

10–3 

Areas of Polygons 



Find the area of each polygon in square units. 

1. 2. 3. 

5 units 2 5 units 2 8 units 2 

4. 5. 6. 


7. 8. 9. 


Estimate the area of each polygon in square units. 10–12. Sample answers given. 

10. 11. 12. 


13. Sketch two polygons that both Sample answer: 

have a perimeter of 20 units, 

but that have different areas. 

14. Sketch a pentagon with an Sample answer: 

area of 20 square units. 

P � 20 

A � 25 

P � 20 

A � 21 


5 

5 

3 

7

10–4 



Areas of Triangles and Trapezoids 

Find the area of each triangle or trapezoid. 

1. 2. 3. 

20 ft 

37 ft 

14 cm 


20 cm 

370 ft 2 140 cm 2 35 m 2 

4. 5. 6. 

5 in. 

12 in. 

30 in 2 70 ft 2 399 cm 2 

7. 8. 9. 

28 cm 

19 mm 

24 mm 

5 ft 

7 ft 

15 ft 

11 m 

3 m 

3 m 

2 cm 3 cm 

22 cm 6 cm 

5 m 

6 m 

8 m 

19 cm 

16 cm 26 cm 

17 in. 

228 mm 2 21 m 2 297 in 2 

10. 11. 12. 

308 cm 2 12 cm 2 225 m 2 

13. Find the area of a trapezoid whose altitude measures 8 feet and whose bases are 9 feet 

and 21 feet long. 120 ft 2 

14. Find the area of a triangle whose base measures 17 inches and whose altitude is 10 

inches. 85 in 2 

15. Find the area of a trapezoid whose altitude measures 77 meters and whose bases are 200 

meters and 300 meters long. 19,250 m 2 

16. The area of a triangle is 500 square feet. The height of the altitude is 25 feet. What is the 

length of the base? 40 ft 

25 m 

18 m 

27 in. 

5 in.

10–5 

24 in. 

12 cm 18 cm 4 ft 

2.5 cm 



Areas of Regular Polygons 

Find the area of each regular polygon. 

1. 2. 3. 

540 cm 2 60 ft 2 360 in 2 

4. 5. 6. 

3 cm 

38 in. 

24 in. 

28 in. 


7 in. 

15 ft 

12 ft 

13 m 

22 in. 

22.5 cm 2 231 in 2 168 m 2 

Find the area of the shaded region in each regular polygon. 

7. 8. 9. 

1824 in 2 270 ft 2 80 m 2 

10. 11. 12. 

1344 in 2 351 m 2 177 cm 2 

18 m 

5 ft 

9 in. 

7 m 

10 in. 

6 m 

30 cm 

13 cm 

8 m 

5 m 

18 cm 

17 cm

10–6 

Symmetry 



Determine whether each figure has line symmetry. If it does, draw all lines of symmetry. If 

not, write no. 

1. 2. 3. 

yes no yes 

4. 5. 6. 

yes no yes 

Determine whether each figure has rotational symmetry. Write yes or no. 

7. 8. 9. 

yes no yes 

10. 11. 12. 

yes no no 


10–7 

Tessellations 



Identify the figures used to create each tessellation. Then identify the tessellation as regular, 

semi–regular, or neither. 

1. 2. 

trapezoids; neither rhombi; neither 

3. 4. 

equilateral triangles and regular hexagons; regular 

right triangles; neither 

5. 6. 

squares and isosceles right trapezoids and rectangles; 

triangles; neither neither 

Create a tessellation using the given polygons. 

7. right triangles 8. equilateral triangles and rhombi 


11–1 



Parts of a Circle 

Use �A at the right to determine whether each statement is true or false. 

1. A�T� is a radius of �A. true 

2. �R�B� is a chord of �A. false 

3. ZU � 2(ZA) true 

4. SA � SW false 

5. AT � BX false 

6. S�W� is a diameter of �A. true 

7. S�W� is a chord of �A. true 

8. AT � AZ true 

9. A�T� is a chord of �A. false 

10. SU � RX false 

11. SA � AU true 

12. S�Y� is a chord of �A. true 

13. SC � SA false 

14. Z�U� is a chord of �A. true 

15. Z�U� is a radius of �A. false 

16. B�U� is a chord of �A. false 

Circle W has a radius of 15 units, and �Z has a radius of 10 units. 

17. If XY � 7, find YZ. 3 

18. If XY � 7, find WX. 8 

19. If XY � 7, find TX. 23 

20. If XY � 7, find WR. 28 


Y 

T 

Z 

R 

B 

A 

S 

X W 

W 

C 

X Y 

U 

Z 

T 

R

11–2 



Arcs and Central Angles 

Find each measure in �C if m�ACB � 80, mAF � � 45, and A�E� and F�D� are diameters. 

1. m�ACF 45 2. mAB 

� 80 

3. m�FCE 135 4. mEF 

� 135 

5. mABE 

� 180 6. m�BCE 100 

7. mAFE 

� 180 8. m�DCE 45 

9. mDE 

� 45 10. m�BCD 55 

11. mBAE 

� 260 12. mABF 

� 315 

In �A, B�D� is a diameter, m�BAE � 85, and m�CAD � 120. Determine whether each 

statement is true or false. 

13. m�BAC � 60 true 

14. mCD 

� � m�CAD true 

15. �ABE is a central angle. false 

16. m�BAC � m�DAE false 

17. mCED 

� � 220 false 

18. mBCD 

� � 180 true 

19. mCE 

� � 145 true 

20. m�DAE � mDE 

� true 

Q is the center of two circles with radii Q�D� and Q�E�. If m�AQE � 90 and mRE � � 115, 

find each measure. 

21. mAE 

� 90 22. m�RQE 115 

23. mAR 

� 155 

25. mAER 

24. m�RQA 155 

� 205 26. mBSD 

� 270 

27. mDS 

� 115 28. mBD 

� R 

S 

Q 

B 

A 

90 

D 


A 

B 

F 

E 

C 

B 

E 

C 

A 

D 

E 

D

11–3 

Arcs and Chords 

Complete each sentence. 



1. If SG 

� � RE 

� , then S�G� � ? R�E� 

2. If ST 

� � ET 

� , then �SMT � � ? EMT 

3. If T�M� ⊥ R�G�, then RT 

� � ? TG � 

4. If ST 

� � TE 

� , S�T� � ? T�E� 

5. If R�G� ⊥ A�S�, then S�B� � ? A�B� 

6. If RE 

� � SG 

� , then �RME � � ? GMS 

7. If R�E� � S�G�, then RE 

� � ? SG � 

8. If T�M� ⊥ R�G�, then ST 

� � ? TE 

� 

9. If T�M� ⊥ R�G�, then S�Q� � ? E�Q� 

10. If T�M� ⊥ R�G� and ST 

� � TE 

� , then �SQT � � ? EQT 

11. If S�Q� � E�Q�, then T�M� ⊥ ? R�G� 

12. If SR 

� � AR 

� , then R�G� ⊥ ? S�A� 

Use �B, where B�X� ⊥ W�Y�, to complete each sentence. 

13. If BW � 23, then BY � ? 23 

14. If WY � 38, then WZ � ? 19 

15. If WZ � 15, then WY � ? 30 

16. If BZ � 6 and WZ � 8, then WB � ? 10 

17. If WB � 15 and BZ � 9, then WZ � ? 12 

18. If WY � 40 and BZ � 15, then WB � ? 25 

19. If BY � 30 and BZ � 18, then WY � ? 48 

20. If mWY 

� � 110, then mWX 

� � ? 55 


R 

W 

S 

Q 

T 

B M 

X 

A 

Z 

B 

Y 

E 

G

11–4 

Inscribed Polygons 

Use �O to find x. 



1. WM � x � 8, ZN � 2x � 5 3 

2. WM � 3x � 10, ZN � 2x � 15 5 

3. WM � x � 6, ZN � 2x � 12 6 

4. WM � 2x � 5, ZN � x � 5 10 

5. WM � 5x � 1, ZN � 2x � 5 2 

6. WM � 4x � 15, ZN � 3x � 19 4 

7. WM � x � 8, ZN � 2x � 5 3 

8. WM � 4x, ZN � 3x � 1 1 

9. WM � x � 1, ZN � 2x � 7 6 

10. WM � 20x � 100, ZN � 30x � 80 2 

Square SQUR is inscribed in �C with a radius of 20 meters. 

11. Find m�SCQ. 90 

12. Find SQ to the nearest tenth. 28.3 m 

13. Find CA to the nearest tenth. 14.2 m 


M 

S 

P 

W Z 

O Q 

A 

C 

N 

Q 

R U

11–5 



Circumference of a Circle 

Find the circumference of each object to the nearest tenth. 

1. a round swimming pool 2. a circular top of a 3. the circular base of a 

with radius 12 feet trampoline with paper weight with 

75.4 ft diameter 16 feet diameter 3 centimeters 

50.3 ft 9.4 cm 

4. a CD with diameter 5. circular garden with 6. circular mirror with 

11 centimeters radius 10 feet diameter 4 feet 

34.6 cm 62.8 ft 12.6 ft 

Find the circumference of each circle to the nearest tenth. 

7. r � 7 cm 8. d � 20 yd 9. r � 1 m 

44.0 cm 62.8 yd 6.3 m 

10. d � 6 ft 11. r � 200 ft 12. d � 5 in. 

18.8 ft 1256.6 ft 15.7 in. 

13. r � 2 m 14. d � 70 ft 15. r � 3 in. 

12.6 m 219.9 ft 18.8 in. 

16. d � 10 in. 17. r � 19 m 18. d � 35 yd 

31.4 in. 119.4 m 110.0 yd 

Find the radius of each circle to the nearest tenth for each circumference given. 

19. 100 m 

15.9 m 

20. 32 ft 

5.1 ft 

21. 18 mi 

2.9 mi 

22. 28 cm 23. 80 in. 24. 25 m 

4.5 cm 12.7 in. 4.0 m 

25. 75 yd 26. 14 cm 27. 250 ft 

11.9 yd 2.2 cm 39.8 ft 


11–6 

Area of a Circle 



Find the area of each circle to the nearest hundredth. 

1. r � 10 in. 2. r � 18 cm 3. r � 4 mm 

314.16 in 2 1017.88 cm 2 50.27 mm 2 

4. d � 50 ft 5. d � 6 in. 6. d � 30 m 

1963.50 ft 2 28.27 in 2 706.86 m 2 

7. C � 31.42 yd 8. C � 131.95 m 9. C � 232.48 ft 

78.56 yd 2 1385.51 m 2 4300.92 ft 2 

10. r � 1 mi 11. d � 90 m 12. C � 628.32 ft 

3.14 mi 2 6361.73 m 2 31,416.07 ft 2 

13. d � 300 ft 14. r � 6 in. 15. C � 150.80 m 

70,685.83 ft 2 113.10 in 2 1809.64 m 2 

A circle has a radius of 10 inches. Find the area of a sector whose central angle has 

the following measure. Round to the nearest hundredth. 

16. 90° 17. 30° 18. 120° 

78.54 in 2 26.18 in 2 104.72 in 2 

19. 45° 20. 60° 21. 135° 

39.27 in 2 52.36 in 2 117.81 in 2 

22. 100° 23. 150° 24. 70° 

87.27 in 2 130.90 in 2 61.09 in 2 


12–1 

Solid Figures 

D 

E 

B 

F 


Name the faces, edges, and vertices of each polyhedron. 

1. A C 

2. J I 

3. 

G 

N 

K L 


H 

M 

H 

O 

T 

S R 

Faces: rectangles Faces: rectangles Faces: �OSR, �ORP, 

ABED, BCFE, ACFD, GHLK, HIML, JIMN, �OTP, �OTS; 

�ACB, �DEF Edges: GJNK, JIHG, NMLK rectangle STPR 

A�C�, D�F�, A�D�, B�E�, C�F�, Edges: G�H�, H�L�, K�L�, Edges: S�O�, R�O�, P�O�, 

A�B�, B�C�, D�E�, E�F� G�K�, G�J�, K�N�, J�N�, J�I�, O�T�, S�R�, R�P�, P�T�, T�S� 

Vertices:A, B, C, D, I�M�, N�M�, H�I�, L�M� Vertices: O, T, P, R, 

E, F Vertices: G, H, K, L, S 

J, I, M, N 

Name each solid. 


4. 5. 6. 

cylinder cube or rectangular triangular prism 

prism 

Determine whether each statement is true or false for the solid. 

7. The figure is a prism. false 

8. The base of the figure is a pentagon. true 

9. There are five lateral faces. true 

10. The figure has 6 edges. false 

D 

I 

G F 

P 

E

12–2 


Surface Areas of Prisms and Cylinders 

Find the lateral area and the surface area for each solid. Round to the nearest 

hundredth, if necessary. 

1. 2. 3. 

100.53 cm 2 ; 760 ft 2 ; 1240 ft 2 48 m 2 ; 60 m 2 

201.06 cm 2 

4. 5. 6. 

904.78 in 2 ; 16 yd 2 ; 24 yd 2 84 in 2 ; 180 in 2 

1306.90 in 2 

7. 20 cm 

8. 9. 

12 cm 

4 cm 

4 cm 

18 in. 

8 in. 

720 cm 2 ; 912 cm 2 471.24 ft 2 ; 1884.96 ft 2 84 ft 2 ; 150 ft 2 

10. 11. 12. 

28 m 


16 cm 15 cm 

16 m 

18 cm 

2 yd 

30 ft 

1407.43 m 2 ; 864 cm 2 ; 1296 cm 2 1866.11 mm 2 ; 

1809.56 m 2 2375.04 mm 2 


2 yd 

5 ft 15 ft 

24 cm 

2 yd 

8 ft 

12 cm 

10 ft 

3 m 

3 ft 

6 in. 

3 ft 

33 mm 

5 m 

4 m 

18 mm 

11 ft 

8 in. 

4 m 

3 in.

12–3 



Volumes of Prisms and Cylinders 

Find the volume of each solid. Round to the nearest hundredth, if necessary. 

1. 2. 3. 

10,618.58 in 3 1000 ft 3 30 in 3 

4. 5. 6. 

4750.09 ft 3 1584 cm 3 28 ft 3 

7. 8. 9. 

26 in. 

20 in. 

13 in. 

42 ft 

17 in. 

6 ft 

9025.80 in 3 6000 in 3 36 m 3 

10. 11. 12. 

7 ft 

2 ft 

6 cm 

3 m 

10 ft 

21.99 ft 3 165 m 3 20,480 ft 3 


10 ft 

10 ft 

22 cm 

4 cm 

20 in. 

8 in. 15 in. 

11 m 

5 m 

3 in. 

3 m 

32 ft 

4 in. 

7 ft 

4 m 

6 m 

32 ft 

20 ft 

5 in. 

4 ft 

1 ft

12–4 



Surface Areas of Pyramids and Cones 

Find the lateral area and the surface area of each regular pyramid or cone. Round to 

the nearest hundredth, if necessary. 

1. 2. 3. 

42 ft 2 ; 51 ft 2 898.50 cm 2 ; 575 m 2 ; 675 m 2 

1278.63 cm 2 

4. 5. 6. 

43.98 ft 2 ; 56.55 ft 2 3840 cm 2 ; 4864 cm 2 30,536.28 in 2 ; 

36,697.16 in 2 

7. 8. 9. 

28 ft 

672 ft 2 ; 840 ft 2 276.46 in 2 ; 477.52 in 2 18,750 cm 2 ; 

24,375 cm 2 

10. 11. 12. 

4 mi 

2 ft 

7 ft 

7 ft 

3 ft 

7 ft 8 ft 

10 mi 

11 cm 

9 cm 

32 cm 

8 in. 

62.83 mi 2 ; 75.40 mi 2 324 cm 2 ; 405 cm 2 31.42 km 2 ; 

43.98 km 2 


26 cm 

60 cm 

11 in. 

18 cm 

54 in. 

125 cm 

4 km 

23 m 

4 m 10 m 

180 in. 

75 cm 

5 km

12–5 



Volumes of Pyramids and Cones 

Find the volume of each solid. Round to the nearest hundredth, if necessary. 

1. 2. 3. 

3 in. 

6 in 3 4712.39 cm 3 12,000 ft 3 

4. 9 mm 

5. 6. 

2120.58 mm 3 80 yd 3 7.33 mi 3 

7. 8. 9. 

22 in. 

3 in. 

4 in. 

2640 in 3 1407.43 ft 3 1680 cm 3 

10. 11. 12. 

66 in. 

36 in. 

25 mm 

24 in. 

15 in. 

6 ft 

41,054.33 in 3 24 ft 3 3.14 ft 3 

6 yd 

8 ft 

3 ft 

20 cm 

15 cm 


21 ft 

4 ft 

8 yd 

2 yd 

14 cm 

1 mi 

40 ft 

7 mi 

3 cm 

30 ft 

24 cm 

30 cm 

2 cm

12–6 

Spheres 



Find the surface area and volume of each sphere. Round to the nearest hundredth. 

1. 2. 3. 

9 m 

1017.88 m 2 ; 2827.43 in 2 ; 5026.55 ft 2 ; 

3053.63 m 3 14,137.17 in 3 33,510.32 ft 3 

4. 5. 6. 

2 mi 70 km 2 in. 

12.57 mi 2 ; 4.19 mi 3 61,575.22 km 2 ; 50.27 in 2 ; 33.51 in 3 

1,436,755.04 km 3 

7. 8. 9. 

10 mm 

1256.64 mm 2 ; 2463.01 ft 2 ; 31,415.93 mi 2 ; 

4188.79 mm 3 11,494.04 ft 3 523,598.78 mi 3 

10. 11. 12. 

28 ft 

15 in. 

60 ft 6 cm 

100 mi 

11,309.73 ft 2 ; 452.39 cm 2 ; 502,654.82 m 2 ; 

113,097.34 ft 3 904.78 cm 3 33,510,321.64 m 3 


40 ft 

400 m

12–7 



Similarity of Solid Figures 

Determine whether each pair of solids is similar. 

1. 2. 

yes yes 

3. 4. 

yes no 

5 6. 

20 m 

yes no 

Find the scale factor of the solid on the left to the solid on the right for each pair of 

similar solids. Then find the ratios of the surface areas and the volumes. 

7. 8. 

2 

� 1 

24 m 

8 m 

10 in. 

20 in. 

40 m 

32 m 

30 m 

6 m 

18 m 10 in. 

30 m 

5 in. 

10 in. 

16 m 

60 m 

45 m 

; ; ; ; 343 

4 8 

7 49 

� � � � � 

1 1 

8 64 512 


3 mm 

4 cm 

8 cm 

6 mm 

5 mm 

7 ft 8 ft 

15 in. 

5 cm 

13 cm 

12 mm

13–1 



Simplifying Square Roots 

Simplify each expression. 

1. �9� 3 2. �169 � 13 3. �400 � 20 4. �225 � 15 

5. �256 � 16 6. �900 � 30 7. �289 � 17 8. �2500 � 50 

9. �44 � 2�11� 10. �18� 3�2� 11. �75� 5�3� 12. �300 � 10�3� 

13. �98� 7�2� 14. �90� 3�10� 15. �125 � 5�5� 16. �80� 4�5� 

17. �250 � 5�10� 18. �12� � �5� 2�15� 19. �6� � �6� 6 20. �10� � �2� 

2�5� 

21. What is the square root of 625? 25 

22. Multiply �17� � �3�. �51� 

23. Write �3� � �15� in simplest form. 3�5� 


13–2 

45°-45°-90° Triangles 



Find the missing measures. Write all radicals in simplest form. 

1. 2. 3. 

9 

45° 

y 

45° 

x 

2 

45° 

x 

45° 

x � 9, y � 9�2� x � 2, y � 2�2� x � 16, y � 16�2� 

4. 5. 6. 

1 

45° 

x 

45° y 

x � �2�, y � 1 x � 32�2�, y � 32 x � 50�2�, y � 50 

7. 8. 9. 

x 45° 10√2 

x � 10, y � 10 x � 14, y � 14 x � 1, y � 1 

10. 11. 12. 

y 

45° 

45° 

y 

x 

50√2 

45° 

y 

y 

45° 

14√2 

32 

45° 

7√2 

45° 

y 

x � 50, y � 50 x � 7�2�, y � 14 x � 5, y � 5 

x 

45° 

x 

45° y 

x 

45° 


y 

16 

45° 

x 45° 

45° 

y 

x 

x 

45° 

45° √2 y 

45° 

x 

50 

5√2 

45° 

y 

45°

13–3 


30°-60°-90° Triangles 

Find the missing measures. Write all radicals in simplest form. 

1. 2. 3. 

y 

30° 

x 

60° 

5 

x � 10, y � 5�3� x � 42, y � 21�3� x � 18, y � 9�3� 

4. 5. 29 

6. 

17 

60° 

x 

y 

30° 

x � 17�3�, y � 34 x � 29�3�, y � 58 x � 15, y � 15�3� 

7. 8. 9. 

y 30° 

42 

60° 

x 

x � 21, y � 21�3� x � 22, y � 22�3� x � 13�3�, y � 13 

10. 11. 12. 

y 30° 10√3 

60° 

x 

x � 10, y � 20 x � 19, y � 38 x � 28, y � 14 

13. 14. 15. 

x 

60° 

y 30° 12 


x 

y 

30° 

60° 

60° 

21 

x � 4�3�, y � 8�3� x � 11�3�, y � 22�3� x � 16�3�, y � 24 


y 

x 

60° 44 

y 

19√3 30° 

y 

30° 

60° 

x 

30° y 

33 

60° 

x 

x 

30° 

x 

60° 

9 

60° 

x 

y 

y 

60° 

26 

y 

30° 

30 

30° 

30° 

y 

60° 

14√3 

30° x 

8√3 

60° 

x 30° y 

x

13–4 

Tangent Ratio 



Find each tangent. Round to four decimal places, if necessary. 

A 

15 

E 

20 

25 

C 

1. tan A 1.3333 2. tan Y 0.5333 3. tan S 0.2917 

4. tan C 0.75 5. tan X 1.875 6. tan R 3.4286 

Find each missing measure. Round to the nearest tenth. 

7. 8. 13 ft 

9. 

x cm 

Z Y 

30 

14.6 15.5 6.9 

10. 11. 12. 

68.6 26.6 71.6 

13. 5 yd 

14. 15. 

5 yd 

26° 

30 cm 

x m 

x° 

55° 

48 m 

X 

16 

x ft 

11 ft 

45 51.8 22.6 

x° 

78° 

34 

50° 

60 ft 

x ft 

30 ft 

T 48 

S 


R 

14 

90 m 

50 

20° 

19 in. 

x° 

x° 

30 m 

12 m 

x in. 

5 m

13–5 


Sine and Cosine Ratios 

Find each sine or cosine. Round to four decimal places, if necessary. 

A 25 

B 

11 

C 

29 

F 20 

1. sin B 0.3793 2. cos C 0.3793 3. cos B 0.8621 

4. sin D 0.7143 5. sin F 0.7143 6. cos G 0.3500 

Find each missing measure. Round to the nearest tenth. 

7. 8. 40 m 

9. 

x ft 

14.9 17.8 57.6 

10. 11. 74 m 

12. 

5 cm 

52° 

x cm 

3.1 71.6 68.2 

13. 19 mm 

14. 15. 

23 mm 

34 ft 

55.7 35.5 25.4 

28 

26° 42 m 

x° 


78 m 

70 km 


D 

20 

E 

86 km 

x° 

x° 

G 

14 

40 

K 36 H 

x° 

15 cm 

28 cm 

x° 78 in. 84 in. 

x° 

x° 

7 ft 

3 ft

14–1 

Inscribed Angles 


Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle. 

1. �XMY no; XY 

� 

2. �RST yes; RT � 

3. �MCN no; MN � 

M 

Y 

A 


4. m�EDA 55 5. mDE � 84 

6. m�BDA 35 7. m�BDE 90 

8. m�ZYW 35 9. mVZ 

� 90 

10. m�XYV 25 11. mWY 

� 80 

12. mXY 

� 70 13. m�XZY 35 

Find the value of x in each circle. 

X 

14. 15. 16. 

A 

(7x � 8)° 

D 

E 

C 

B 

(6x � 1)° 

9 28 6 

17. x° 

18. (3x � 5)° 

19. 

V 

Y 

80° 

Z 

X 


W 

160 20 3 

S 

(2x � 4)° 

M 

R 

E 

R 

B 

© Glencoe/McGraw-Hill 79 Geometry: Concepts and 

N 

D 

P 

O 

T 

(x � 5)° 

B 

D 

(x � 10)° 

Q 

C 

42° 

M 110° 

70° 

A 

E 

(9x � 4)° 

P 

(8x � 4)° 

C 

C 

O 

M 

V 

40° 

X 

R 

N 

X 

50° 

Z 

R 

B 

A 

M 

P 

(8x � 2)° 

70° 

N 

45° 

Exercises 4–7 Exercises 8–13 

W 

(6x � 2)° 

Y

14–2 


Tangents to a Circle 

Find each measure. Round to the nearest tenth if necessary. Assume segments that 

appear to be tangent are tangent. 

1. BC 2. DF 3. SR 

3 in. 

A B 

5 in. 

C 

11 cm 

13 cm 

4 in. 24 cm 50 ft 

4. m�BAC 5. m�ARC 6. EG 

66 25 21 

7. m�ZAY 8. FE 9. MR 

X 

X 

A 

A 

Y 

C 

10° 

48° 

B 

80 14 cm 35 in. 

10. BC 11. HG 12. m�XZY 

A 

16 m 

D 

B 

30 m 


C 

Z 

18 m 4 mi 45 

E 

D 

C 


G 

65° 

H 

A 

E 

F 

A 

7 cm 

B 16 cm 

F 

X 

D 

30 cm 

4 mi 

G I 

J 

R 

C 

R 

Q 

50 ft 

P R 

G 

S 

S 

15 in. 

E 28 cm 

F 

X 

Z 

P 

O 

M 

20 in. 

N 

Y 

35 cm

14–3 

Secant Angles 




1. m�EFB 2. m�ABC 3. m�LPM 

58 22 78 

4. m�XYZ 5. m�CED 6. mWZ 

� 

30 26 36 

7. mFE � 

E 

Z 

8. mSQ � 

9. mAE � 

10 47 142 

Find the value of x in each circle. Then find the given measure. 

10. mBC � 

F 

70° 

B 

A 

D 46° C 

X 

120° 60° 

T 

110° 

D 

C 

50° 

90° 

A 

G 

F E 

D 

Y 

B 

A 28° 

95° 

11. mHG � 

A 46° F 

E 

C 

E 

9x° 

7x° 

B 

R 

W 

12. mJL 

� 

10; 70 7; 52 5; 32 

C 

A 

80° P 36° 

G 

M 

K 


E 

S 

24° 

Q 

7x° 

H 

C 

24° 

D 

G 

T 

(7x � 3)° 

B 

K 

71° 

Y 

44° 

X 

P 

36° 

B D 

70° 

76° 

M 

A 

I 

C 

N 

H 

O 

P 

40° 

Q 

Z 

E 

L 

W 

M 

J 

L 

85° 

K 

(6x � 2)° 

(4x � 2)°

14–4 



Secant-Tangent Angles 

Find the measure of each angle. Assume segments that appear to be tangent are tangent. 

1. �1 2. �2 3. �ABC 

70° 

25 50 125 

4. �3 5. �4 6. �XYZ 

56 45 120 

7. �5 8. �6 9. �CDE 

5 

124° 

3 

150° 

20° 1 

30 27 90 

10. �7 11. �TUY 12. �8 

118° 

7 

230° 

62 135 22 

4 

100° 

70° 

6 

46° 

T 

160° 


90° 

U 

Y 

2 

X 

A 

C 

D 

Y 

110° 

112° 

120° 

B 

Z 

E 

8 

C

14–5 



Segment Measures 

Find the value of x in each circle. If necessary, round to the nearest tenth. 

1. 2. 3. 

3 6 

7 x 

14 13.5 10 

4. 5. 6. 

11 4 

x 

5 

7 4 26 

7. 8. 9. 

4 12 32 

Find each measure. If necessary, round to the nearst tenth. 

10. DE 11. IH 12. WX 

A 

12 

18 

12 

B 

13 

x 

6 

E 

C 

10 

D 

6 

9 9 

20 16 6 

F 

x 

6 

7 

24 

I 


x 

2 

x 

9 

G 

8 

H 

18 

Z 

15 

18 

x 

6 8 

24 

X 

x 

x 

5 

12 

12 

Y 

10 

4 

W

14–6 



Equations of Circles 

Write an equation of a circle for each center and radius or diameter measure given. 

1. (1, 1), r � 2 2. (�3, 2), d � 2 

(x � 1) 2 � (y � 1) 2 � 4 (x � 3) 2 � (y � 2) 2 � 1 

3. (�1, �5), r � 3 4. (4, �3), d � 4 

(x � 1) 2 � (y � 5) 2 � 9 (x � 4) 2 � (y � 3) 2 � 4 

5. (0, 2), r � 4 6. (5, 0), r � 1 

x 2 � (y � 2) 2 � 16 (x � 5) 2 � y 2 � 1 

7. (0, 0), r � 6 8. (�1, 1), d � 6 

x 2 � y 2 � 36 (x � 1) 2 � (y � 1) 2 � 9 

9. (�5, 5), r � 5 10. (�3, 3), d � 20 

(x � 5) 2 � (y � 5) 2 � 25 (x � 3) 2 � (y � 3) 2 � 100 

11. (�6, �1), d � 10 12. (4, 4), d � 14 

(x � 6) 2 � (y � 1) 2 � 25 (x � 4) 2 � (y � 4) 2 � 49 

13. (3, 7), d � 2�2� 14. (�5, 2), r � �6� 

(x � 3) 2 � (y � 7) 2 � 2 (x � 5) 2 � (y � 2) 2 � 6 

15. (0, �2), r � �10 � 16. (7, 0), d � 2�5� 

x 2 � (y � 2) 2 � 10 (x � 7) 2 � y 2 � 5 

Find the coordinates of the center and the measure of the radius for each circle 

whose equation is given. 

17. (x � 5) 2 � (y � 2) 2 � 49 18. (x � 3) 2 � (y � 7) 2 � 100 

(�5, 2), 7 (3, �7), 10 

19. (x � 1) 2 � (y � 8) 2 � 121 20. x 2 � y 2 � 64 

(�1, �8), 11 (0, 0), 8 

21. x 2 � (y � 9) 2 � 81 22. (x � 3) 2 � y 2 � 25 

(0, �9), 9 (�3, 0), 5 

23. (x � 6) 2 � (y � 6) 2 � 36 24. x 2 � y 2 � 5 

(6, �6), 6 (0, 0), �5� 

25. x 2 � (y � 4) 2 � 7 26. (x � 1) 2 � (y � 1) 2 � 10 

(0, 4), �7� (1, �1), �10� 


15–1 


Logic and Truth Tables 

For Exercises 1–16, use conditionals a, b, c and d. 

a: A triangle has three sides. b: January is a day of the week. 

c: 5 � 5 � 20 d: Parallel lines do not intersect. 

Write the statements for each negation. 

1. �a 

A triangle does not have three sides. 

2. �b 

January is not a day of the week. 

3. �c 

5 � 5 � 20 


4. �d 

Parallel lines intersect. 

Write a statement for each conjunction or disjunction. Then find the truth value. 

5. a � b A triangle has three sides or January is a day of the week; true. 

6. a � b A triangle has three sides and January is a day of the week; false. 

7. a � c A triangle has three sides or 5 � 5 � 20; true. 

8. a � c A triangle has three sides and 5 � 5 � 20; false. 

9. a � d A triangle has three sides or parallel lines do not intersect; true. 

10. a � d A triangle has three sides and parallel lines do not intersect; true. 

11. b � c January is a day of the week or 5 � 5 � 20; false. 

12. b � c January is a day of the week and 5 � 5 � 20; false. 

13. b � d January is a day of the week or parallel lines do not intersect; true. 

14. b � d January is a day of the week and parallel lines do not intersect; false 

15. c � d 5 � 5 � 20 or parallel lines do not intersect; true. 

16. c � d 5 � 5 � 20 and parallel lines do not intersect; false. 


15–2 

Deductive Reasoning 



Use the Law of Detachment to determine a conclusion that follows from statements 

(1) and (2). If a valid conclusion does not follow, write no valid conclusion. 

1. (1) If a figure is a triangle, then it is a polygon. 

(2) The figure is a triangle. 

The figure is a polygon. 

2. (1) If I sell my skis, then I will not be able to go skiing. 

(2) I did not sell my skis. 

no valid conclusion 

3. (1) If two angles are complementary, then the sum of their measures is 90. 

(2) Angle A and B are complementary. 

The sum of the measures of angles A and B is 90. 

4. (1) If the measures of the lengths of two sides of a triangle are equal, then the triangle is 

isosceles. 

(2) Triangle ABC has two sides with lengths of equal measure. 

Triangle ABC is isosceles. 

5. (1) If it rains, we will not go on a picnic. 

(2) We do not go on a picnic. 


Use the Law of Syllogism to determine a conclusion that follows from statements 

(1) and (2). If a valid conclusion does not follow, write no valid conclusion. 

6. (1) If my dog does not bark all night, I will give him a treat. 

(2) If I give my dog a treat, then he will wag his tail. 

If my dog does not bark all night, then he will wag his tail. 

7. (1) If a polygon has three sides, then the figure is a triangle. 

(2) If a figure is a triangle, then the sum of the measures of the interior angles is 180. 

If a polygon has three sides, then the sum of the measures of the 

interior angles is 180. 

8. (1) If the concert is postponed, then I will be out of town. 

(2) If the concert is postponed, then it will be held in the gym. 


9. (1) All whole numbers are rational numbers. 

(2) All whole numbers are real numbers. 


10. (1) If the temperature reaches 70°, then the swimming pool will open. 

(2) If the swimming pool opens, then we will not go to the beach. 

If the temperature reaches 70°, then we will not go to the beach. 


15–3 

Paragraph Proofs 



Write a paragraph proof for each conjecture. 

1. If �ABD is an isosceles triangle with base B�D� 

and C is the midpoint of B�D�, then �ACD � 

�ACB. 

If �ABD is an isosceles triangle with base B�D�, then A�D� � A�B�. If C is the 

midpoint of B�D�, then C�D� � C�B�. A�C� � A�C� by the Reflexive Property, so 

�ACD � �ACB by SSS. 

2. If lines a and b are parallel and W�X� � X�Y�, 

then �WXS � �YXZ. 

If lines a and b are parallel, then �SWX � �XYZ since they are alternate 

interior angles. �WXS � �YXZ since they are vertical angles. Then it is 

given that W�X� � X�Y�, so �WXS � �YXZ by ASA. 

3. If ACDE is an isosceles trapezoid with bases 

A�C� and E�D�, then �AED � �CDE. 

If ACDE is an isosceles trapezoid with bases A�C� and E�D�, then the legs 

are congruent, so A�E� � C�D�. Also, an isosceles trapezoid has congruent 

base angles, so �AED � �CDE. Now,E�D� � E�D� by the Reflexive Property, 

so �AED � �CDE by SAS. 

4. If RSTX is a rhombus, then �RXT � �RST. 

If RSTX is a rhombus, then RS � RX and XT � ST. RT � RT by the 

Reflexive Property, so �RXT � �RST by SSS. 


D 

E 

X 

A 

C 

B 

S W 

X 

Y Z 

A C 

B 

R S 

T 

a 

b 

D

15–4 

Complete each proof. 

1. If m�1 � m�2 and m�3 � m�4, then 

m�ABC � m�ROD. 

R 2 

Given: m�1 � m�2, m�3 � m�4 

Prove: m�ABC � m�ROD 

A 

O 

Proof: 

1 

3 

Statements Reasons 

B C 

a. m�1 � m�2, m�3 � m�4 a. Given 

b. m�ABC � m�1 � m�3 

m�ROD � m�2 � m�4 

b. Angle Addition Postulate 

c. m�1 � m�3 � m�2 � m�4 c. Addition Property of Equality 

d. m�ABC � m�ROD d. Substitution Property of Equality 

4 

7x 

� 

6 

2. If � 14, then x � 12. 

7x 

� 

6 

Given: � 14 



Preparing for Two-Column Proofs 

Prove: x � 12 

Proof: 


7x 

a. �� 14 a. Given 

6 

b. 7x � 84 b. Multiplication Property of Equality 

c. x � 12 c. Division Property of Equality 

3. If �ABC is a right triangle with �C a right 

angle and m�A � m�B, then m�A � 45. 

Given: �ABC is a right triangle with �C a 

right angle and m�A � m�B. 

Prove: m�A � 45 

A 

Proof: 

C B 


a. �ABC is a right triangle with �C a a. Given 

right angle and m�A � m�B 

b. m�A � m�B � m�C � 180 b. Angle Sum Theorem 

c. m�C � 90 c. Definition of Right Angle 

d. m�A � m�B � 90 d. Subtraction Property of Equality 

e. m�A � m�A � 90 e. Substitution Property of Equality 

f. 2m�A � 90 f. Substitution Property of Equality 

g. m�A � 45 g. Division Property of Equality 


D

15–5 

Two-Column Proofs 

Write a two-column proof. 


1. Given: �ITC is an isosceles triangle with base 

I�C�, TS �� bisects �ITC 

Prove: I�S� � C�S� 

Proof: 

Statements Sample Answer: Reasons 

a. �ITC is an isosceles triangle a. Given 

with base I�C�. 

b. TS �� bisects �ITC b. Given 

c. I�T� � C�T� c. Definition of isosceles triangle 

d. �ITS � �CTS d. Definition of angle bisector 

e. S�T� � S�T� e. Reflexive Property 

f. �ITS � �CTS f. SAS 

g. I�S� � C�S� g. CPCTC 

2. Given: ABCD is a square. 

Prove: A�C� � B�D� 

Proof: 


Statements Sample Answer: Reasons 

a. ABCD is a square. a. Given 

b. A�D� � B�C� b. Definition of a square 

c. �ADC and �BCD are right c. Definition of a square 

angles. 

d. �ADC � �BCD d. Definition of congruent angles 

e. D�C� � D�C� e. Reflexive Property 

f. ΔADC � ΔBCD f. SAS 

g. A�C� � B�D� g. CPCTC 


I 

D 

T 

S 

A B 

C 

C

15–6 

Coordinate Proofs 


Position and label each figure on a coordinate plane. 1–5. Sample answers given. 

1. a square with sides m units long 

D (0, m) 

O 

y 

C (m, m) 

B (m, 0) 

A (0, 0) 

2. a right triangle with legs p and r units long 

O 

y 

Z (0, r) 

X (0, 0) 

Y (p, 0) 

3. a rhombus with sides c units long 

y 

S (a, d) 

O P (0, 0) 

x 

Q (c, 0) x 

x 

R (c � a, d) 

4. an isosceles triangle with base d units long and heights s units long 

1 A (� 2d, 

0) 

O 

y 

C (0, s) 

1 B ( 2d, 

0) 

x 

5. a rectangle with length x units and width y units 

x 

D (� 2, 

y) 

x 

A (� 2, 

0) 


O 

y 

x 

C ( 2, 

y) 

x 

B ( 2, 

0) 

x 


16–1 


Solve each system of equations by graphing. 

1. y � x 2. y � 2x � 4 3. y � x � 1 

y ��x � 2 (1, 1) y ��x � 1 (�1, 2) y ��x � 5 (�2, �3) 

y 

y � �x � 2 

y � x 

O 

(1, 1) 

x 

(�1, 2) 

4. y � x � 5 5. y � x � 4 6. y ��x 

y ��x � 1 (3, �2) y ��x � 2 (�3, 1) y ��3x � 4 (2, �2) 

O 

y 

y � �x � 1 

y � x � 5 

x 

(3, �2) 

7. y � 2x � 1 8. y � x � 6 9. y � x � 1 

y � 3x � 2 (�1, �1) y ��2x � 6 (4, �2) y ��x � 5 (3, 2) 

y 

y � 3x � 2 

y � 2x � 1 

O x 

(�1, �1) 

O 

10. y � x � 5 11. y � x � 1 12. y ��x � 1 

y ��3x � 1 (�1, 4) y � 2x � 4 (�3, �2) y ��2x � 5 (4, �3) 

y 

y � x � 5 

(�1, 4) 

y � �3x � 1 

O 

x 


Solving Systems of Equations by Graphing 


y 

y � 2x � 4 

y 

y � x � 4 

y � �x � 1 

(�3, 1) 

x 

O x 

y � �x � 2 

y 

y � �2x � 6 

O 

(4, �2) 

y � x � 6 

y 

y � 2x � 4 

x 

y � x � 1 

O x 

(�3, �2) 

y 

y � x � 1 

O x 

(�2, �3) 

y � �x � 5 

y 

y � �3x � 4 

O 

y � �x 

y 

y � �x � 5 

x 

(2, �2) 

(3, 2) 

O 

y � x � 1 

O 

y 

x 

y � �2x � 5 

y � �x � 1 

(4, �3) 

x

16–2 



Solving Systems of Equations by Using Algebra 

Use substitution to solve each system of equations. 

1. y � 7 2. y ��3 3. y � x 

x � 2y � 5 

(7, �1) 

x � y � 8 

(5, �3) 

2x�y�15 (5, 5) 

4. y � x � 7 5. y � x � 2 6. y � x � 1 

2x � 3y � 19 3x � 2y ��4 4x � 3y � 4 

(8, 1) (0, 2) (1, 0) 

7. 3x � y � 2 8. �2x � y � 0 9. 4x � y � �13 

2x � 2y � 8 3x � y � 4 2x � 3y � �11 

(�1, 5) (4, 8) (�2, �5) 

Use elimination to solve each system of equations. 

10. x � y � 7 11. x � y � 4 12. x � y ��3 

x � y � 1 2x � y ��13 3x � y ��5 

(4, 3) (�3, 7) (�2, �1) 

13. x � y � 5 14. x � y ��2 15. x � y � 2 

2x � y � 4 �2x � y ��1 �3x � y ��4 

(3, �2) (3, 5) (1, 1) 


16–3 

Translations 



Find the coordinates of the vertices of each figure after the given translation. Then 

graph the translation image. 

1. (3, 4) 2. (�2, 3) 3. (1, 5) 

A 

C 

O 

B 

y 

A' 

C' 

Q' y 

B' 

x 

Q 

O 

U' 

D' 

A' 

A´(0, 2), B´(2, 3), Q´(�1, 4), U´(2, 2), D´(�2, 4), E´(0, 5), 

C´(1, 5) A´(2, 0), D´(�1, 1) F´(�1, 1) 

4. (3, �2) 5. (�3, �1) 6. (4, 0) 

T 

P 

y 

A P' 

O 

x 

T´(0, 2), R´(2, 2), G´(1, 3), H´(0, 0), A´(0, 2), B´(3, 4), 

A´(2, �1), P´(0, 0) A´(�3, 1) C´(3, �4), D´(1, �3) 

7. (0, �3) 8. (�2, �4) 9. (�5, 0) 

P 

P' 

M 

M' 

R 

O 

T' R' 

y 

A' 

N 

N' 

x 

A' 

V' 

M´(�1, 1), N´(3, 0), R´(0, 1), S´(2, 0), X´(0, 4), Y´(0, 1), 

P´(�3, �2) T´(1, �3), V´(�2, �4) Z´(�4, 1) 


A 

D 

O H' 

R' 

O V 

y 

G' 

H 

G 

x 

U 

A 

x 

y R S 

T' 

T 

S' 

x 

A 

Z' 

D 

D 

D' 

F 

F' 

C 

E 

B 

A' 

O 

X' 

E' y 

O 

y 

D' 

y 

Y' Z 

O 

B' 

C' 

x 

X 

x 

Y 

x

16–4 

Reflections 



Find the coordinates of the vertices of each figure after a reflection over the given axis. 

Then graph the reflection image. 

1. x-axis 2. y-axis 3. x-axis 

A 

A' 

O 

y 

C 

C' 

B 

B' 

x 

X' y X 

y 

D 

Y' Z' Z 

O 

A´(�2, �3), B´(3, �4), X´(�3, 4), Y´(�4, 1), D´(�2, �3), E´(2, �4), 

C´(2, �1) Z´(�1, 1) F´(4, �2), G´(�3, �1) 

4. y-axis 5. x-axis 6. y-axis 

J' 

K' 

I' 

O 

y 

I 

M 

J 

x 

K 

J´(�4, 4), K´(�4, �4), P´(�2, �1), Q´(1, �3), R´(�2, 2), X´(�4, �1), 

M´(�2, �2), I´(�2, 2) R´(4, �2) T´(�1, �3) 

7. x-axis 8. y-axis 9. x-axis 

Z 

Z' 

M' 

W 

W' 

O 

y 

X 

X' 

Y 

x 

Y' 

C' 

D' 

P 

P' 

O 

W´(–1, –3), X´(3, –4), B´(–1, 4), C´(–4, 3), D´(3, –4), E´(2, 0), 

Y´(4, –1), Z´(–2, 0) D´(–3, 1), E´(0, 2) F´(–2, –3) 


y 

Q 

Q' 

B' y B 

E' 

O 

E 

D 

Y 

x 

R 

x 

R' 

C 

x 

X' 

G 

G' 

D' 

R' 

A 

A' 

O 

O 

T' 

O 

y 

T 

y 

R 

E 

E' 

C 

C' 

B 

B' 

F 

x 

F' 

x 

X 

x

16–5 

Rotations 


Find the coordinates of the vertices of each figure after the given rotation about the 

origin. Then graph the rotation image. 

1. 90˚ counterclockwise 2. 90˚ clockwise 3. 180˚ counterclockwise 

B' 

y 

A' A 

O 

B 

x 

R 

A´(�1, 1), B´(�2, 4) S´(1, 1), R´(4, 3) C´(�1, �1), D´(�4, �3) 

4. 180˚ clockwise 5. 90˚ counterclockwise 6. 90˚ clockwise 

E´(�2, 1), F´(�3, 4) G´(�2, 1), H´(�1, 3), J´(4, �2), K´(1, �4), 

I´(0, 0) M´(0, 0) 

7. 180˚ clockwise 8. 90˚ counterclockwise 9. 90˚ clockwise 

P' 

F' 

N' 

E' 

O 

y 

y 

Q' 

O Q 


E 

N 

F 

x 

P 

x 

S 

Q' 

G' 

Q 

S' 

H' 

S 

O 

N´(�2, �3), P´(�4, �1), Q´(�4, �2), R´(0, 0), T´(0, 0), W´(�3, �3), 

Q´(0, 0) S´(�2, �4) X´(�4, �1) 


y 

S' 

y 

OI' I 

y 

G 

R 

O R' 

H 

R' 

x 

x 

x 

D' 

X' 

W' 

y 

C 

C' O 

M 

M' O 

y 

y 

T' T 

O 

K' 

X 

J 

D 

W 

K 

J' 

x 

x 

x

16–6 

Dilations 


Find the coordinates of the dilation image for the given scale factor k, and graph the 

dilation image. 

1. � 1 

� 2. 2 3. �1 

2 3 � 

y 

A´(1, 1), B´(2, 3) Y´(2, 4), Z´(6, 8) C´(1, 2), D´(2, 3) 

4. 4 5. 2 6. � 1 

4 � 

A' 

A 

G G' 

O 

A´(0, 8), C´(8, 8) T´(�2, 6), R´(0, 0), A´(�2, 2), X´(0, 1), 

E´(8, 0), G´(0, 0) I´(�6, 2) E´(�1, 0) 

7. � 1 

� 8. �2 

2 3 

y 

O 

y 

F' 

C 

E 

T' 

B 

B' Z 

Y' 

A 

A' 

Y 

O 

x 

O 

F 

M' 

T 


C' 

E' x 

M 

x 

I' 

y 

I 

R 

O R' 

� 9. 2 

C 

F´(1, �1), M´(3, �2), A´(0, 6), B´(0, 0), R´(�2, 4), S´(2, 6), 

T´(2, �3) C´(�2, 4) T´(4, �2) 


T' 

C' 

T 

y 

y 

A 

A' 

B' 

O B x 

Z' 

x 

x 

A 

O 

y 

C' 

R' 

R 

O 

C 

D' 

E 

y 

S 

A' 

T 

D 

E' O 

S' 

x 

T' 

x 

y 

X 

X' 

x

Visit us online at: 

www.geomconcepts.com 

ISBN 0-07-869312-8 

9 780078693120 

90000

Skills Practice Workbook - Glencoe

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?