Angles and Parallel Lines

12 34

56 78

Corresponding Angle Postulate

If two parallel lines are crossed by a transversal, then each pair of corresponding angles are congruent.

12 34

56 78

Alternate Interior Angles Theorem

If two parallel lines are crossed by a transversal, then each pair of alternate interior angles are congruent.

12 34

56 78

Consecutive Interior Angles Theorem

If two parallel lines are crossed by a transversal, then each pair of consecutive interior angles are supplementary.

12 34

56 78

Alternate Exterior Angles Theorem

If two parallel lines are crossed by a transversal, then each pair of alternate exterior angles are congruent.

12 34

56 78

Perpendicular Transversal Theorem

In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.

a

b

c

Make a sketch of the problem in your notes.

Given j || k,

Angles and Parallel Lines

jk

Applications –

1 2 3 4 5

10

6 7 8 911

1213

14

1 43 , 14 24o om m

3 1.

Corresponds with 1.

43o

9 2.Alternate exterior with 14.

24o

10 3.Linear pair with 9.180o – 24o = 156o

156o

Find the measure of

jk

Given j || k,

Find the measure of

Angles and Parallel Lines

Applications –

1 2 3 4 5

10

6 7 8 911

1213

14

1 43 , 14 24o om m

4 4.

Linear pair with 3.

137o

11 5.Vertical angle with 10.

156o

7 6.Vertical with 1.Alternate Interior of 3.

43o