Geo_Book_Answers

Answers to Exercises
Answers to Exercises
CHAPTER 4 • CHAPTER CHAPTER 4 • CHAPTER
LESSON 4.1
1. The angle measures change, but the sum
remains 180°.
2. 73°
3. 60°
4. 110°
5. 24°
6. 3 360° 180° 900°
7. 3 180° 180° 360°
8. 69°; 47°; 116°; 93°; 86°
9. 30°; 50°; 82°; 28°; 32°; 78°; 118°; 50°
10.
11.
12. First construct E, using the method used in
Exercise 10.
A
13.
E
M
R
A
R
M A
G
L
14. From the Triangle Sum Conjecture
mA mS mM 180°. Because M is a
right angle, mM 90°. By substitution,
mA mS 90° 180°. By subtraction,
mA mS 90°. So two wrongs make a right!
15. Answers will vary. See the proof on page 202.
To prove the Triangle Sum Conjecture, the Linear
Pair Conjecture and the Alternate Interior Angles
Conjecture must be accepted as true.
16. It is easier to draw PDQ if the Triangle Sum
Conjecture is used to find that the measure of
D is 85°. Then PD can be drawn to be 7 cm, and
48 ANSWERS TO EXERCISES
R
Fold
4
G
L
A
E
R
angles P and D can be drawn at each endpoint
using the protractor.
40
85
P 7 cm D
17. The third angles of the triangles also have the
same measures; are equal in measure
18. You know from the Triangle Sum Conjecture
that mA mB mC 180°, and mD
mE mF 180°. By the transitive property,
mA mB mC mD mE mF.
You also know that mA mD, and mB
mE. You can substitute for mD and mE in the
longer equation to get mA mB mC
mA mB mF. Subtracting equal terms
from both sides, you are left with mC mF.
19. For any triangle, the sum of the angle measures
is 180°, by the Triangle Sum Conjecture. Since the
triangle is equiangular, each angle has the same
measure, say x. So x x x 180°, and x 60°.
20. false
21. false
22. false
23. false
55
24. true
25. eight; 100
Q