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Notice that in the Geometry Activity, AE and GF do not intersect. These segments

are not parallel since they do not lie in the same plane. Lines that do not intersect

and are not coplanar are called

skew lines

. Segments and rays contained in skew

lines are also skew.

Identify Relationships

Example

Example

1

1

G

a. Name all planes that are parallel to

F

plane ABG.

B

plane CDE

A

H

Study Tip

b. Name all segments that intersect CH.

E

BC, CD, CE, EH, and GH

Identifying

C

Segments

D

c. Name all segments that are parallel to EF.

Use the segments drawn

AD, BC, and GH

in the figure even though

other segments exist.

d. Name all segments that are skew to BG.

AD, CD, CE, EF, and EH

ANGLE RELATIONSHIPS

t

In the

transversal

drawing of the railroad crossing, notice

t

that the tracks, represented by line

,

m

intersect the sides of the road,

m

n

represented by lines

and

. A line

that intersects two or more lines in

Study Tip

a plane at different points is called a

n

Transversals

transversal

.

The lines that the

transversal intersects

need not be parallel.

Identify Transversals

Example

Example

2

2

AIRPORTS

Some of the runways at O’Hare International Airport are shown

below. Identify the sets of lines to which each given line is a transversal.

q

a. line

q

If the lines are extended, line

n

p

n

p

r

intersects lines ,

,

, and

.

m

b. line

m

n

p

r

lines ,

,

, and

n

c. line

Control Tower

q

lines ,

m

,

p

, and

q

r

d. line

m

p

q

lines ,

,

, and

r

t

In the drawing of the railroad crossing above, notice that line

forms eight angles

m

n

with lines

and

. These angles are given special names, as are specific pairings of

these angles.

Lesson 3-1 Parallel Lines and Transversals 127

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