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Proving Lines Parallel

•

Recognize angle conditions that occur with parallel lines.

•

Prove that two lines are parallel based on given angle relationships.

do you know that the sides of

do you know that the sides of

a parking space are parallel?

a parking space are parallel?

Have you ever been in a tall building and

looked down at a parking lot? The parking

lot is full of line segments that appear to be

parallel. The workers who paint these lines

must be certain that they are parallel.

IDENTIFY PARALLEL LINES

When each stripe of a parking space intersects

the center line, the angles formed are corresponding angles. If the lines are parallel,

we know that the corresponding angles are congruent. Conversely, if the

corresponding angles are congruent, then the lines must be parallel.

Postulate 3.4

Postulate 3.4

If two lines in a plane are cut by a transversal so that

m

corresponding angles are congruent, then the lines

1

2

are parallel.

3

4

If corr.

are

, then lines are

Abbreviation:

.

n

5

6

If

1

5,

2

6,

3

7,

Examples:

7

8

or

4

8, then m n.

Postulate 3.4 justifies the construction of parallel lines.

Parallel Line Through a Point Not on Line

Use a straightedge to

Copy

PMN so that

Draw PQ. Because

2

2

3

1

1

3

draw a line. Label two

P is the vertex of the

RPQ

PMN by

Study Tip

points on the line as

new angle. Label the

construction and they

Look Back

M and N. Draw a

intersection points

are corresponding

To review copying angles,

point P that is not

Q and R.

angles, PQ MN.

see Lesson 1-4.

on MN. Draw PM.

Lesson 3-5 Proving Lines Parallel 151

David Sailors/CORBIS

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Parent category: Education