Geo_Book_Answers

Answers to Exercises
LESSON 2.5
1. a 60°, b 120°, c 120°
2. a 90°, b 90°, c 50°
3. a 77°, b 52°, c 77°, d 51°
4. a 60°, b c 120°, d f 115°, e 65°,
g i 125°, h 55°
5. a 90°, b 163°, c 17°, d 110°, e 70°
6. The measures of the linear pair of angles add up
to 170°, not 180°.
7. The angles at which he should cut measure 45°.
8. Greatest: 120°. Smallest: 60°. One possible
explanation: The tree is perpendicular to the
horizontal. The angle of the hill measures 30°.
The smaller angle and the angle between the hill
and the horizontal form a pair of complementary
angles, so the smaller angle equals 90° 30° 60°.
The smaller angle and larger angle form a linear
pair, so the larger angle equals 180° 60° 120°.
9. The converse is not true. ; sample counterexample:
A
55
125
B
10. each must be a right angle
11. Let the measures of the congruent angles be x.
They are supplementary, so x x 180°, 2x 180°,
x 90°. Thus each angle is a right angle.
12. The ratio is 1. The ratio does not change as
long as the lines don’t coincide. Because the
demonstration does not explain why, it is not
a proof.
13. P
14.
3
A
5
28 ANSWERS TO EXERCISES
T
22. (Lesson 2.5)
15.
16.
17.
6
18. Possible answer: All the cards look exactly as
they did, so it must be the 4 of diamonds, because
it has rotational symmetry while the others do not.
19. 22.5°
20.
21. C n H 2n
H H
H C C
H H
22. See table below.
23. handshake problem: n(n 1)
2
pieces of string
24. 3160 intersections
25. n(n 2)
2 yields 760 handshakes.
26. 21; 252
27. n(n 3)
2
3 4
H
C
H
H
C
H
H
C
H
80( 79)
;
2
560; there are 35 vertices.
28. M is the midpoint of AY;deductive.
Rectangle 1 2 3 4 5 6 … n … 200
Perimeter of rectangle 10 14 18 22 26 30 … 4n 6 … 806
O
A
T
H
C
H
C
H
H
C
H
3160
Number of squares 6 12 20 30 42 56 … … 40,602
(n 1)(n 2)