4.5 Introduction to Parallel LinesObjectives:

Recognize planesRecognize transversals and angle pairsRecognize parallel lines

Plane: extends in two directions, usually represented by a shape that looks like a tabletop or wall.

DC

BA M

Plane M or plane ABC

Coplanar: any objects, lines, points, etc., that lie in the same plane.

Noncoplanar: any objects, lines, points, etc., that do not lie in the same plane.

Transversal: a line that intersects two coplanar lines but not concurrently.

interior

exterior

Corresponding angles: angles on the same side of the transversal, but one is in the interior and the other in the exterior.

1 24 3

5 68 7

1

5

2

6

3

7

4

8

1 24 3

5 68 7

Alternate interior angles: angles on opposite sides of the transversal and in the interior.

4

6

3

5

1 24 3

5 68 7

Alternate exterior angles: angles on opposite sides of the transversal and in the exterior.

1

7

2

8

1 24

58 7

Same side interior angles: angles on the same side of the transversal and in the interior.

4

5

3

6

3

6

1 24 3

5 68 7

Same side exterior angles: angles on the same side of the transversal and in the exterior.

1

8

2

7

1

24

3

5

68

7

Example 1: Find:a) All corresponding angles

b) All same side interior angles

c) All alternate exterior angles

d) All alternate interior angles

e) All same side exterior angles

Example 2: Find:a) All corresponding angles

b) All same side interior angles

c) All alternate exterior angles

d) All alternate interior angles

e) All same side exterior angles

1

34

5

2

68 7

l1

l2

l3

912 11

10

Example 3: Name the numbered angles:

41

23

12 3

4

5

6

A transversal must be a side in each angle!

Example 4: Name some angles:

EC

FA B

D

Parallel lines: Two coplanar lines that do not intersect.

C

A B

D