3-1

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NAME
3-1
DATE
PERIOD
Study Guide and Intervention
Parallel Lines and Transversals
Relationships Between Lines and Planes When two
n
Example
P
Q
โ„“
m
S
R
Refer to the figure at the right to identify each of the following.
a. all planes parallel to plane ABD
plane EFH
b. all segments parallel to ๐‘ช๐‘ฎ
B
๐ต๐น , ๐ท๐ป, ๐ด๐ธ
C
F
c. all segments skew to ๐‘ฌ๐‘ฏ
G
A
D
๐ต๐น, ๐ถ๐บ, ๐ต๐ท, ๐ถ๐ท, and ๐ด๐ต
E
H
Exercises
Refer to the figure at the right to identify each of the following.
1. all planes that intersect plane OPT
N
O
2. all segments parallel to ๐‘๐‘ˆ
U
M
3. all segments that intersect ๐‘€๐‘ƒ
T
P
R
S
Refer to the figure at the right to identify each of the following.
4. all segments parallel to ๐‘„๐‘‹
5. all planes that intersect plane MHE
N
M
E
H
Q
6. all segments parallel to ๐‘„๐‘…
T
7. all segments skew to ๐ด๐บ
O
X
R
A
S
G
Chapter 3
5
Glencoe Geometry
Lesson 3-1
lines lie in the same plane and do not intersect, they are parallel.
Lines that do not intersect and are not coplanar are skew lines.
In the figure, โ„“ is parallel to m, or โ„“ โˆฅ ๐‘š You can also
write ๐‘ƒ๐‘„ โˆฅ ๐‘…๐‘†. Similarly, if two planes do not intersect, they
are parallel planes.
NAME
3-1
DATE
PERIOD
Study Guide and Intervention
(continued)
Parallel Lines and Transversals
Angle Relationships A line that intersects two or more other lines at two different
points in a plane is called a transversal. In the figure below, line t is a transversal. Two
lines and a transversal form eight angles. Some pairs of the angles have special names. The
following chart lists the pairs of angles and their names.
Angle Pairs
Name
โˆ 3, โˆ 4, โˆ 5, and โˆ 6
interior angles
โˆ 3 and โˆ 5; โˆ 4 andโˆ 6
alternate interior angles
โˆ 3 and โˆ 6; โˆ 4 and โˆ 5
consecutive interior angles
โˆ 1, โˆ 2, โˆ 7, and โˆ 8
exterior angles
โˆ 1 and โˆ 7; โˆ 2 and โˆ 8;
alternate exterior angles
โˆ 1 and โˆ 5; โˆ 2 and โˆ 6;
โˆ 3 and โˆ 7; โˆ 4 and โˆ 8
corresponding angles
t
1 2
4 3
5 6
8 7
Example
Classify the relationship between each pair of
angles as alternate interior, alternate exterior, corresponding,
or consecutive interior angles.
a. โˆ 10 and โˆ 16
m
n
p
1 2
4 3
5 6
8 7
b. โˆ 4 and โˆ 12
alternate exterior angles
q
9 10
12 11
13 14
16 15
n
โ„“
corresponding angles
c. โˆ 12 and โˆ 13
d. โˆ 3 and โˆ 9
consecutive interior angles
alternate interior angles
Exercises
Use the figure in the Example for Exercises 1โ€“12.
Identify the transversal connecting each pair of angles.
1. โˆ 9 and โˆ 13
2. โˆ 5 and โˆ 14
3. โˆ 4 and โˆ 6
Classify the relationship between each pair of angles as alternate interior,
alternate exterior, corresponding, or consecutive interior angles.
4. โˆ 1 and โˆ 5
5. โˆ 6 and โˆ 14
6. โˆ 2 and โˆ 8
7. โˆ 3 and โˆ 11
8. โˆ 12 and โˆ 3
9. โˆ 4 and โˆ 6
10. โˆ 6 and โˆ 16
11. โˆ 11 and โˆ 14
12. โˆ 10 and โˆ 16
Chapter 3
6
Glencoe Geometry
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