Preparing for the Regents Examination Geometry, AK
Preparing for the Regents Examination Geometry, AK Preparing for the Regents Examination Geometry, AK
2 18,000 180(n 2) n 2 100 n 102 3 Diagonals n 3 a 0 b 1 c 2 d 4 e 8 4 Triangles n 2 a 7 b 10 c 15 d 98 5 180n a 720 b 900 c 1,160 d 3,420 6 sum _ 180 a 1,000 sides b 100 sides 7 360 _ n a 40 b 36 c 10 d 5 360 8 __ # of degrees a 12 b 10 c 6 d 8 180(n 2) 9 # of degrees _ n a 18 b 360 c 8 d 6 10 sum 180(n 2) a 12 b 24 c 50 d 1,000 11 Each exterior angle is 30. 360 _ 12 sides 30 12 180(n 2) 720 180n 360 720 180n 1,080 n 6 180(n 2) 13 _ 8 360 n _ n 180(n 2) 2,880 n 2 16 n 18 14 m1 70, m2 75, m3 105, m4 145 15 m1 90, m2 110, m3 70, m4 35, m5 95, m6 85 16 m1 m2 m6 120 m3 m4 m5 60 17 180(n 2) 5(360) n 12 18 (5x 10) (6x 25) (6x 25) (5x 10) (3x 5) 180(3) 25x 65 540 x 19 Interior angles: 105, 139, 139, 105, 52 19 x + 3x + 4x + 4x + 6x 360 18x 360 x 20 Exterior angles: 20, 60, 80, 80, 120 Interior angles: 160, 120, 100, 100, 60 20 (3x 4) (7x 7) (6x 5) (5x 8) (3x 2) 5x 360 29x 348 x 12 Exterior angles: 40, 91, 67, 68, 34, 60 Interior angles: 140, 89, 113, 112, 146, 120 Chapter Review (pages 212–216) 1 a no slope b 1 _ 4 c 15 _ 7 d 5 _ 2 e 3 _ 5 f 0 2 a 2 b 1 c no slope d 0 e 7 _ 5 f no slope 3 ___ 3 m AC _ 5 ___ , m BC 5 _ . Slopes are negative 3 reciprocals. ___ 4 m SL m ___ BC m ___ PS m ___ 1. Opposite sides LA are parallel (slopes are equal) and slopes of consecutive sides are negative reciprocals (sides are perpendicular). ___ 5 m PL m ___ AN 1 and m ___ PS m ___ 4. LA Opposite sides are parallel (slopes are equal). 6 For parallel lines m and n cut by transversal a, m6 m10. So 2y 3y 10, and y 38. m1 m6 m9 m14 76 m2 m5 m10 m13 104 For parallel lines m and n cut by transversal b, m4 m12. So 2y 15 3y 7, and y 22. m4 m7 m12 m15 59 m3 m8 m11 m16 121 7 m1 42, m2 48, m3 42, m4 42 8 mx 85 9 mx 60 10 mx 68 11 130 Chapter Review 53
12 a mx 45, my 45 b mx 98, my 82 c mx 60, my 70 d mx 65, my 52 e mx 67, my 78 f mx 15, my 55 g mx 55, my 62.5 13 a 5 b 20 c 35 d 594 e n 3 _ 2 14 102 sides 15 8 sides 16 14 sides 17 6 sides 18 a mx 85 b my 55 19 mD 45 20 m1 m2 25 21 m1 140 Note: Since there are many variations of proofs, the following is simply one set of acceptable statements to complete each proof. Depending on the textbook used, the wording and format of reasons may differ, so they have not been supplied for the method of congruence applied in each problem. (These solutions are intended to be used as a guide—other possible solutions may vary.) 22 1. 6 4 2. x y 3. x z 4. y z (Transitive postulate) 23 1. 2 4 2. 1 3 3. 1 2 3 4 4. m r (Corresponding angles are congruent.) 24 1. ___ QR ___ PS 2. QPS QRS 3. RPS QRP 4. QPS RPS QRS QRP or QRP SRP 5. ___ QP ___ RS (Corresponding angles are congruent.) 25 1. ___ BC bisects ABD. 2. 2 3 3. 1 2 4. 1 3 (Transitive postulate) 5. 5 1 54 Chapter 9: Parallel Lines 6. 3 5 7. a b (Alternate interior angles are congruent.) 26 1. ___ AC bisects BCD. 2. 3 4 3. ___ AB ___ BC 4. ABC is a right angle. 5. ___ CD ___ AD 6. CDA is a right angle. 7. ___ AC ___ AC 8. I II (Hypotenuse–acute angle) 27 1. ABCD 2. ___ CF ___ DE 3. ACF BDE 4. ___ CF ___ DE 5. ___ AB ___ CD 6. ___ AB ___ BC ___ CD ___ BC 7. ___ AC ___ BD 8. ACF BDE (SAS SAS) 9. ___ AF ___ BE 28 1. ___ BE bisects ABC. 2. DBE EBA 3. ___ DE ___ BA 4. DEB EBA (Alternate interior angles are congruent.) 5. DEB DBE (Transitive postulate) 6. ___ DB ___ DE 7. BDE is isosceles. (Definition of isosceles triangle) 29 1. ___ AF 2. ___ AB ___ CD 3. ___ AC ___ EF 4. ___ AC ___ CE ___ EF ___ CE 5. ___ AE ___ CF 6. ___ AB ___ CD 7. BAE DCF (Corresponding angles are congruent.) 8. BAE DCF (SAS SAS) 9. ___ BE ___ DF (CPCTC) 30 1. ___ AB ___ CB 2. A C 3. B B 4. ABE CBD (ASA ASA) 5. ___ AE ___ CD 31 1. ___ BA ___ AE 2. BAE is a right angle. 3. 1 2 4. B D
- Page 5 and 6: 1-4 Angles (pages 9-10) 1 (4) It is
- Page 7 and 8: 6 True 7 True 8 True 9 True 10 Answ
- Page 9 and 10: 3 1. e ∨ ~f 2. ~f → g 3. ~e 4.
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- Page 13 and 14: 6. BAC DAE 6. Transitive property.
- Page 15 and 16: CHAPTER 4-1 Setting Up a Valid Proo
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- Page 39 and 40: 11. mABC mADC 12. 2mABD 2mADB 13.
- Page 41 and 42: 6. mDAB mCAD mDCB mACD 7. mCAB
- Page 43 and 44: g e 17 a _ f d b Undefined c a _
- Page 45 and 46: 5 BIG is isosceles because it has t
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- Page 61 and 62: 7. MAD RCB 8. MAD RCB (SAS SAS)
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- Page 105 and 106: Chapters 1-5 (pages 446-449) Part I
2 18,000 180(n 2)<br />
n 2 100<br />
n 102<br />
3 Diagonals n 3<br />
a 0 b 1 c 2<br />
d 4 e 8<br />
4 Triangles n 2<br />
a 7 b 10 c 15 d 98<br />
5 180n<br />
a 720 b 900 c 1,160 d 3,420<br />
6 sum _<br />
180<br />
a 1,000 sides b 100 sides<br />
7 360 _<br />
n<br />
a 40 b 36 c 10 d 5<br />
360<br />
8 __<br />
# of degrees<br />
a 12 b 10 c 6 d 8<br />
180(n 2)<br />
9 # of degrees _<br />
n<br />
a 18 b 360 c 8 d 6<br />
10 sum 180(n 2)<br />
a 12 b 24 c 50 d 1,000<br />
11 Each exterior angle is 30. 360 _ 12 sides<br />
30<br />
12 180(n 2) 720<br />
180n 360 720<br />
180n 1,080<br />
n 6<br />
180(n 2)<br />
13 _ 8 360<br />
n<br />
_<br />
n<br />
180(n 2) 2,880<br />
n 2 16<br />
n 18<br />
14 m1 70, m2 75, m3 105,<br />
m4 145<br />
15 m1 90, m2 110, m3 70,<br />
m4 35, m5 95, m6 85<br />
16 m1 m2 m6 120<br />
m3 m4 m5 60<br />
17 180(n 2) 5(360)<br />
n 12<br />
18 (5x 10) (6x 25) (6x 25) <br />
(5x 10) (3x 5) 180(3)<br />
25x 65 540<br />
x 19<br />
Interior angles: 105, 139, 139, 105, 52<br />
19 x + 3x + 4x + 4x + 6x 360<br />
18x 360<br />
x 20<br />
Exterior angles: 20, 60, 80, 80, 120<br />
Interior angles: 160, 120, 100, 100, 60<br />
20 (3x 4) (7x 7) (6x 5) (5x 8) <br />
(3x 2) 5x 360<br />
29x 348<br />
x 12<br />
Exterior angles: 40, 91, 67, 68, 34, 60<br />
Interior angles: 140, 89, 113, 112, 146, 120<br />
Chapter Review (pages 212–216)<br />
1 a no slope<br />
b 1 _<br />
4<br />
c 15 _<br />
7<br />
d 5 _<br />
2<br />
e 3 _<br />
5<br />
f 0<br />
2 a 2<br />
b 1<br />
c no slope<br />
d 0<br />
e 7 _<br />
5<br />
f no slope<br />
3<br />
___ 3 m AC _ 5<br />
___ , m BC <br />
5 _ . Slopes are negative<br />
3<br />
reciprocals.<br />
___ 4 m SL m ___<br />
BC m ___<br />
PS m ___ 1. Opposite sides<br />
LA<br />
are parallel (slopes are equal) and slopes of<br />
consecutive sides are negative<br />
reciprocals (sides are perpendicular).<br />
___ 5 m PL m ___<br />
AN 1 and m ___<br />
PS m ___ 4.<br />
LA<br />
Opposite sides are parallel (slopes are<br />
equal).<br />
6 For parallel lines m and n cut by transversal<br />
a, m6 m10. So 2y 3y 10, and<br />
y 38.<br />
m1 m6 m9 m14 76<br />
m2 m5 m10 m13 104<br />
For parallel lines m and n cut by transversal<br />
b, m4 m12. So 2y 15 3y 7,<br />
and y 22.<br />
m4 m7 m12 m15 59<br />
m3 m8 m11 m16 121<br />
7 m1 42, m2 48, m3 42, m4 42<br />
8 mx 85<br />
9 mx 60<br />
10 mx 68<br />
11 130<br />
Chapter Review 53
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