3-1 Parallel Lines and Transversals3-1 Parallel Lines and Transversals3-1 Parallel Lines and Transversals3-1 Parallel Lines and Transversals

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You used angle and line segment relationships to prove theorems.

• Identify relationships between two lines or two planes.

• Name angle pairs formed by parallel lines and transversals.

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Parallel LinesParallel lines are lines in the same plane that never intersect.

-8 -6 -4 -2

2

42 6 8

4

6

-4

-6

-8

-2

8

Parallel lines have the same slope.

Example 1Determine whether these lines are parallel.y = 4x -6

and y = 4x + 2

The slope of both lines is 4.

So, the lines are parallel.

Skew Lines

Skew lines are lines that do not intersect and are not coplanar.

A

B

m

n

B. Name a segment skew to EH.

Answer: AB, CD, BG, or CF

Parallel Planes

Parallel planes are planes that do not intersect.

A

B

C. Name a plane parallel to plane ABG.

Answer: plane CDE

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Transversal DefinitionA transversal is a line that

intersects two coplanar lines at two different points.

Exterior

Exterior

Interior

1 234

5 6

78

r

s

Transversal t

Angles formed by Transversals

Consecutive interior angles

5&4

1 2

34

5 6

78

6&3

interior

Angles formed by Transversals

Alternate interior angles

6&4 5&3

1 2

34

5 6

78

interior

Angles formed by Transversals

Alternate exterior angles

7&1

1 2

34

5 6

78

8&2

exterior

exterior

Angles formed by Transversals

Corresponding angles

5&1

1 2

34

5 6

78

6&2 7&3 8&4

Classify Angle Pair Relationships

A. Classify the relationship between 2 and 6 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.

Answer: corresponding

B. Classify the relationship between 1 and 7 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.

Answer: alternate exterior

C. Classify the relationship between 3 and 8 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.

Answer: consecutive interior

D. Classify the relationship between 3 and 5 as alternate interior, alternate exterior, corresponding, or consecutive interior angles.

Answer: alternate interior

A. BUS STATION The driveways at a bus station are shown. Identify the transversal connecting 1 and 2. Then classify the relationship between the pair of angles.

Answer: The transversal connecting 1 and 2 is line v. These are corresponding angles.

B. BUS STATION The driveways at a bus station are shown. Identify the transversal connecting 2 and 3. Then classify the relationship between the pair of angles.

Answer: The transversal connecting 2 and 3 is line v. These are alternate interior angles.