Geo_Book_Answers

Answers to Exercises
LESSON 5.4
1. three; one 2. 28
3. 60°; 140° 4. 65°
5. 23 6. 129°; 73°; 42 cm
7. 35 8. See flowchart below.
9. Parallelogram. Draw a diagonal of the original
quadrilateral. The diagonal forms two tri-angles.
Each of the two midsegments is parallel to the
diagonal, and thus the midsegments are parallel to
each other. Now draw the other diagonal of the
original quadrilateral. By the same reasoning, the
second pair of midsegments is parallel. Therefore,
the quadrilateral formed by joining the midpoints is
a parallelogram.
10. The length of the edge of the top base
measures 30 m. We know this by the Trapezoid
Midsegment Conjecture.
11. Ladie drives a stake into the ground to create a
triangle for which the trees are the other two
vertices. She finds the midpoint from the stake to
each tree. The distance between these midpoints is
half the distance between the trees.
12. Explanations will vary.
80
Cabin
40 60
60 cm
8. (Lesson 5.4)
64 ANSWERS TO EXERCISES
1
2
FOA with
midsegment LN
Given
IOA with
midsegment RD
Given
3
4
LN OA
?
Triangle Midsegment Conjecture
OA RD
?
13. If a quadrilateral is a kite, then exactly one
diagonal bisects a pair of opposite angles. Both the
original and converse statements are true.
14. a 54°, b 72°, c 108°, d 72°, e 162°,
f 18°, g 81°, h 49.5°, i 130.5°, k 49.5°,
m 162°, n 99°; Possible explanation: The third
angle of the triangle containing f and g measures
81°, so using the Vertical Angles Conjecture, the
vertex angle of the triangle containing h also
measures 81°. Subtract 81° from 180° and divide by
2 to get h 49.5°. The other base angle must also
measure 49.5°. By the Corresponding Angles
Conjecture, k 49.5°.
15. (3, 8)
16. (0, 8)
17. coordinates: E(2, 3.5), Z(6, 5); the slope of
EZ 3
8 ,and the slope ofYT 3
8
18.
F
R
K
N
There is only one kite, but more than one way to
construct it.
Triangle Midsegment
Conjecture
5
LN RD
?
Two lines parallel to the
same line are parallel