Geo_Book_Answers

LESSON 5.3
1. 64 cm 2. 21°; 146° 3. 52°; 128°
4. 15 cm 5. 72°; 61° 6. 99°; 38 cm
7. w 120°, x 45°, y 30°
8. w 1.6 cm, x 48°, y 42°
9. See flowchart below.
10. Answers may vary. This proof uses the Kite
Angle Bisector Conjecture.
Y
2
B N
1 X
E
Given: Kite BENY with vertex angles B and N
Show: Diagonal BN is the perpendicular bisector
of diagonal YE.
From the definition of kite, BE BY.From the
Kite Angle Bisector Conjecture, 1 2. BX
BX because they are the same segment. By SAS,
BXY BXE. So by CPCTC, XY XE.
Because YXB and EXB form a linear pair, they
are supplementary, so mYXB mEXB
180°. By CPCTC, YXB EXB, or mYXB
mEXB, so by substitution, 2mYXB 180°, or
mYXB 90°. So mYXB mEXB 90°.
Because XY XE and YXB and EXB are right
angles, BN is the perpendicular bisector of YE.
11. possible answer: E I
I
12. possible answer:
Z I
Q U
The other base is ZI . Q and U are a pair of base
angles. Z and I are a pair of base angles.
9. (Lesson 5.3)
1 BE BY
Given
2 EN YN
3
Given
BN BN
Same segment
?
?
T
E
K
13. possible answer:
OW is the other base. S and H are a pair of
base angles. O and W are a pair of base angles.
SW HO .
14. Only one kite is possible
F
because three sides determine
a triangle.
N
B
15.
E
16. infinitely many, possible construction:
E
W O
S H
I
B O
S H
N
W
17. 80°, 80°, 100°, 100°
18. Because ABCD is an isosceles trapezoid, A
B. AGF BHE by SAA. Thus, AG BH
by CPCTC.
19. a 80°, b 20°, c 160°, d 20°, e 80°,
f 80°, g 110°, h 70°, m 110°, n 100°;
Possible explanation: Because d forms a linear pair
with e and its congruent adjacent angle,d 2e
180°.Substituting d 20° gives 2e 160°,so e 80°.
Using theVerticalAngles Conjecture and d 20°, the
unlabeled angle in the small right triangle measures
20°, which means h 70°. Because g and h are a
linear pair, they are supplementary, so g 110°.
?
5 1 and
3
6
and
?
? 4
Congruence
shortcut
Definition of
angle bisector
?
BEN ?
?
?
BYN 2 BN bisects B, BN bisects N
SSS
4
CPCTC
ANSWERS TO EXERCISES 63
Answers to Exercises