EXERCISES
For more exercises, see Extra Practice.
Practice and Problem Solving
A
Practice by Example
Name the indicated figures in each diagram.
Example 1
(page 459)
A
B
Z
C
R
1. three points
F
4. all points Z R, F
2. three different segments
5. all segments ZR, RF , ZF
3. four different rays
6. all lines See left.
BC
A
B
D
H
C
y.
7. all segments
C
8. all lines
10. all rays
)
9. all rays
Example 2
(page 460)
11. all points
Name all indicated segments.
E
D
G
F
B
C
D
Super
Crunch
Cereal
L
M
K
N
12–17. See left.
A
P
S
I
J
Q
R
H
K
W
12. that intersect DE
15. that intersect MN
13. that are parallel to DE
16. that are parallel to MN
14. that are skew to DE
17. that are skew to MN
Packaging For the cereal box (left), name each of the following.
18. four segments that intersect AE
F
E
G
H
Example 3
(page 460)
19. three segments parallel to AE
20. four segments skew to AE
21. Use notebook paper or graph paper. Draw three segments
that are parallel to each other. Draw a line that intersects
the parallel segments.
* )
23. Draw VB .
22. Draw two parallel rays.
* )
24. Draw CD so that it intersects two segments, FG and HJ.
B
Apply Your Skills
Modeling Draw each of the following. If not possible, explain.
* ) * )
25. PQ 6 RS
9-1
)
26. AB 6 BC
*
)
27. JK skew to LM
Introduction to Geometry: Points, Lines, and Planes
461-463
S
T
U
V
X
W
28. ■ 6 XY
29. ■ 6 YZ
30. ■ 6 WX
31. ■ 6 SV
Complete with always, sometimes, or never to make a true statement.
Y
Z
Use the figure at the left. Name a segment to make each
statement true.
)
)
)
)
32. AB and BC are 9 on the same line.
33. AB and AC are 9 the same ray.
34. AX and XA are 9 the same segment.
* )
* )
35. TQ and QT are 9 the same line.
36. Skew lines are 9 in the same plane.
37. Two lines in the same plane are 9 parallel.
Algebra
38.
Write an equation. Then find the length of each segment.
2x
39.
3
6
12x ⫹ 1
8x
2x – 3
40.
4x ⫹ 1
5x
6 – 5x – 4x – 1
8x; 1, 3, 4
12x – 1; 6, 10, 9, 25
Writing in Math Explain what the symbols AB and AB represent.
Use examples. See left.
)
)
41. Error Analysis A student says that AB is the same ray as BA .
Explain the student’s error.
C
Challenge
C Street
ue
B Street
h
ft
Fi
en
Av
Main Street
42. City Planning
Use the map. Tell
whether the streets
in each pair appear
to be parallel or
intersecting.
a. N.W. Highway
and Fifth Avenue
b. N.W. Highway
and B Street
c. A and C Streets
N.
W
.H
ig
hw
ay
A Street
d. B and C Streets
e. C and Main Streets
a–e. See left.
43. a. Suppose a town installs a mailbox at a point P. How many
straight roads can the town build leading to P?
b. Suppose a town installs mailboxes at points P and R.
How many straight roads might the town build that pass
by both mailboxes?
44. a. On a coordinate plane, draw a line through Q 2 12, 21 R and
Q 1, 112 R . Then draw a line through (-1, 1) and Q 12, 312 R . See left.
b. What appears to be true of the two lines that you drew in
part (a)?
l
c. Find the slope of each line. 53, 53
d. Inductive Reasoning Make a conjecture based on your answer
to parts (b) and (c).
461-463
Chapter 9 Spatial Thinking
Test Prep
Multiple Choice
F
E
A
G
H
B
D
C
Take It to the NET
Online lesson quiz at
www.PHSchool.com
Web Code: ada-0901
Short Response
Use the figure at the left for Exercises 45–48.
45. Which segment is skew to AB?
A. BC
B. CD
C. DE
D. GC
46. Which segment is parallel to ED?
F. BH
G. AF
H. AB
I. GE
47. Which segment does NOT intersect AG?
A. AB
B. GC
C. AF
D. BC
48. Which describes BHDC?
F. point
G. line
I. ray
H. plane
49. Draw a line and label three of its points as A, B and C.
g
g
a. Explain why both AB and BA are names for your line.
b. State another name for your line.
Mixed Review
Lesson 8-8
Graph each inequality in its own coordinate plane.
50. y $ -2x + 6
Lessons 5-3 and 5-4
51. y . x + 1
52. x # -4
Simplify each expression.
7
53. 38 + 12
57. 5 ? 3
8 4
54. 234 - 15
6
3
2
58. 2 3
8
55. 11 + 21
3
6
1
59. 1 ? 3
4
56. 21 - 32
3
2
3
60. 4 4
8
Choreographer
Choreographers are usually experienced dancers whose
hard work and dedication have earned them the
opportunity to create original dances. Choreographers
have an excellent sense of timing and spatial positioning.
Many choreographed dance numbers reflect geometric
shapes such as triangles and quadrilaterals. Next time
you see a dance group perform, be on the lookout for
geometry—it will help you think like a choreographer!
Take It to the NET For more information about
choreographers, go to www.PHSchool.com.
Web Code: adb-2031
9-1
Introduction to Geometry: Points, Lines, and Planes
461–463