Name ________________________________________ Date ___________________ Class __________________
CHAPTER
8
Section Quiz
Lessons 8-1 Through 8-3
Choose the best answer.
Use the figure for Exercises 6 and 7.
1. What is the length of the altitude to the
hypotenuse in a right triangle if this
altitude divides the hypotenuse into
segments of lengths 8 millimeters and 18
millimeters?
A 12 mm
C 26 mm
B 13 mm
D 36 mm
6. What is tan K?
F
8
17
H
15
17
G
8
15
J
15
8
Use the figure for Exercises 2 and 3.
7. To the nearest degree, what is m∠M?
2. If XY = 10 and XW = 12, what is VY?
F 2
H 12
G 4.4
J 14.4
C 12
B 4
D 13
4. To estimate the height
of a flagpole, Marci, who
is 5 feet tall, stands so
that her lines of sight to
the top and bottom of
the pole form a 90°
angle. What is the
height of the pole to
the nearest foot?
F 9 ft
H 25 ft
G 20 ft
J 50 ft
C 62°
B 28°
D 88°
8. A 24-foot ladder forms a 76° angle with
the ground. The top of the ladder rests
against a building. To the nearest inch,
how high up the building does the ladder
reach?
3. If XY = 9 and VW = 6, what is VX?
A 3
A 2°
F 5 ft 10 in.
H 18 ft 5 in.
G 18 ft 1 in.
J 23 ft 3 in.
9. What is cos 30°?
A
B
1
3
3
2
C
D
2
3
3
10. To the nearest degree, what is the
measure of the smallest angle of a right
triangle whose legs measure 9 and 15?
5. One acute angle of a right triangle
measures 28°. To the nearest tenth, what
is the length of the side opposite that
angle if the hypotenuse measures 16
meters?
F 31°
H 53°
G 37°
J 59°
11. To the nearest degree, what angle does a
hill with a grade of 11% make with a
horizontal line?
A 7.5 m
C 18.1 m
A 6°
C 79°
B 14.1 m
D 34.1 m
B 11°
D 84°
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
145
Holt Geometry
DF = ( −4 − 4)2 + (0 − 2)2 = 2 17
6. Yes; since UABC ∼ UPQR and
UPQR ∼ UYQX, then UABC ∼ UYQX
by the Transitive Property of Similarity.
EF = ( −2 − 4)2 + ( −4 − 2)2 = 6 2
AB
5
1 BC 3 2 1
=
= ,
=
= ,
DE 2 5 2 EF 6 2 2
Cumulative Test
AC
17
1
=
= . So all three
DF 2 17 2
corresponding sides are proportional.
Therefore, UABC ∼ UDEF by SSS ∼ .
and
Performance Assessment
1. a. 16
b. 12
2. 4 : 3
4
3. Yes; the slope of BC is , and the slope
3
3
4 ⎛ 3⎞
of AB is − . Since i ⎜ − ⎟ = −1,
4
3 ⎝ 4⎠
AB ⊥ BC, so m∠ABC = 90°.
4. Possible answer: P(13, 8); other answer:
P(13, −10)
5. a. X(9, −1)
b. Possible answer: Y(13, 2); other
answer: Y(13, −4)
3
c. yes; slope of XY = slope of PR = or
4
3
− so XY PR. Then ∠PRQ ≅ ∠YXQ
4
and ∠RPQ ≅ ∠XYQ because
corresponding angles of lines are
congruent. So, UPRQ ∼ UYXQ
by AA ∼ .
1. B
23. B
2. H
24. J
3. D
25. D
4. G
26. H
5. A
27. B
6. F
28. G
7. D
29. B
8. H
30. F
9. C
31. C
10. J
32. H
11. B
33. A
12. J
34. J
13. A
35. C
14. G
36. H
15. D
37. C
16. H
38. G
17. D
39. D
18. H
40. J
19. C
41. D
20. G
42. G
21. D
43. C
22. F
CHAPTER 8
Section Quiz: Lessons 8-1 Through 8-3
1. A
5. A
9. B
2. G
6. G
10. F
3. C
7. C
11. A
4. H
8. J
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
266
Holt Geometry