Geo_Book_Answers

Answers to Exercises
5. See flowchart below.
6. Given: ABC with BA BC, CD AD
Show: BD is the angle bisector of ABC.
B
1
2
A
C
BA BC CD AD BD BD
Given Given
Same segment
ABD CBD
SSS
1 2
CPCTC
→
BD bisects ABC
Definition of angle
bisector
7. The angle bisector does not go to the midpoint
of the opposite side in every triangle, only in an
isosceles triangle.
8. NE, because it is across from the smallest angle
in NAE. It is shorter than AE, which is across
from the smallest angle in LAE.
9. The triangles are congruent by SSS, so the two
central angles cannot have different measures.
10. PRN by ASA; SRE by ASA
11. Cannot be determined. Parts do not
correspond.
56 ANSWERS TO EXERCISES
D
5. (Lesson 4.7)
1
2
SA NE
?
?
Given
SE NA
Given
3
4
5
3 4
AIA Conjecture
SN SN
12. ACK by SSS
13. a 72°, b 36°, c 144°, d 36°, e 144°,
f 18°, g 162°, h 144°, j 36°, k 54°,
m 126°
14. The circumcenter is equidistant from all three
vertices because it is on the perpendicular bisector
of each side. Every point on the perpendicular
bisector of a segment is equidistant from the
endpoints. Similarly, the incenter is equidistant
from all three sides because it is on the angle
bisector of each angle, and every point on an angle
bisector is equidistant from the sides of the angle.
15. ASA. The fishing pole forms the side.
“Perpendicular to the ground” forms one angle.
“Same angle on her line of sight” forms the other
angle.
16. 2
7
17.
18. y
4
Y
X
B O
B' Y'4
?
? 6
?
? 7
?
?
?
1 2
ESN ANS
SA NE
AIA Conjecture ASA
CPCTC
Same segment
O'
This proof shows that in a parallelogram,
opposite sides are congruent.
X'
x