Geometry 5.Review Answers (textbook)

Additional Resources
Assessment Book
Chapter Test, Levels A, B, C
• Standardized Chapter Test
• SAT/ACT Chapter Test
• Alternative Assessment
•
Test Generator
5
4. 2;
n SWV > n UWV
so SV 5 UV.
CHAPTER TEST
Two midsegments of n ABC are }
DE and }
DF.
1. Find DB. 10
EF is a midsegment.
What can you conclude about }
EF? }
3.
5. 3; since }
QS
bisects PSR
the Angle
Find the value of x. Explain your reasoning.
Bisector Theorem
5.
4.
guarantees
T
P
PQ 5 RQ.
6x
Chapter Test
Easily-readable reduced copies (with answers) of Chapter
Test B, the Standardized
Chapter Test, and the
Alternative Assessment from
the Assessment Book can be
found on pp. 292G–292H.
B
2. Find DF. 13
10
26
E
D
A
F
C
6.
H
3x 1 9
(5x 2 4)8
6. 7; since J is
G
S
U
(4x 1 3)8 J
interior to HGK
W
P
R
2x 1 11
8x 2 1
and equidistant
V
from each side
S
K
of the angle,
}
the Converse
7. In Exercise 4, is point T on the perpendicular bisector of SU? Explain.
of the Angle
Yes; n STU is isosceles.
Y
Bisector Theorem 8. In the diagram at the right, the angle bisectors
B
guarantees
of n XYZ meet at point D. Find DB. 7
A
m HGJ 5 m KGJ.
25
D
13.
X
C
22
A
Z
18
In the diagram at the right, P is the centroid of n RST.
36
18.
24
C
B
R
J
your
house
10. If TP 5 20, find TJ and PJ. 30, 10
7 mi
S
9. If LS 5 36, find PL and PS. 12, 24
P
L
K
11. If JR 5 25, find JS and RS. 25, 50
9 mi
T
movie
theater
beach
12. Is it possible to construct a triangle with side lengths 9, 12, and 22?
market
If not, explain why not. No; the sum of the lengths of any two sides of a triangle
must be greater than the length of the third side.
13. In n ABC, AB 5 36, BC 5 18, and AC 5 22. Sketch and label the triangle.
List the angles in order from smallest to largest. A, B, C ; see margin for art.
14. }
MJ; the
Hinge Theorem
guarantees the
longer side is
opposite the
larger angle.
15. LJK ; the
Converse of the
Hinge Theorem
guarantees the
larger angle is
opposite the
longer side.
In the diagram for Exercises 14 and 15, JL 5 MK. See margin.
14. If m JKM > m LJK, which is longer, }
LK or }
MJ ? Explain.
K
M
16. Write a temporary assumption you could make to prove the
conclusion indirectly: If RS 1 ST Þ 12 and ST 5 5, then RS Þ 7. Assume that RS 5 7.
Use the diagram in Exercises 17 and 18.
17. Describe the range of possible distances from the beach
to the movie theater. 2 mi < d < 16 mi
18. A market is the same distance from your house, the
your house
7 mi
movie
theater
9 mi
beach
Chapter 5 Relationships within Triangles
lage11se-0580.indd 348
348
J
15. If MJ < LK, which is larger, LJK or JKM? Explain.
movie theater, and the beach. Copy the diagram and
locate the market. See margin.
348
L
6/19/09
lage11se2

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