Lesson 5.3

Congruent Angles Associated with Parallel

Lines

Most Theorems in this section are converses of what we learned in sec 5-2

In this section we start with parallel lines then state the special pairs of angles

Parallel Postulate: Through a point not on a line, there is exactly one parallel to the given line.

a

P

Notice the special tick marks ( ) used to designate parallel lines.

Six Theorems About Parallel Lines

If two parallel lines are cut by a transversal, then• Each pair of alternate interior angles are

congruent

• Each pair of alternate exterior angles are congruent

• Each pair of corresponding angles are congruent

• Each pair of interior angles on the same side of the transversal are supplementary

• Each pair of exterior angles on the same side of the transversal are supplementary.

Solve

Since alt. int. s are , 3x + 5 = 2x + 10 x + 5 = 10 x = 5

3(5) + 5 = 20Because vertical s are , m1 = 20.

1.FA ║ DE2. A D3.FA DE4.AB CD5.AC BD6.ΔFAC ΔEDB7. F E

1.Given2.║ lines → alt. int. s 3.Given4.Given5.Addition Property (BC to

step 4)

6.SAS (3, 2, 5)

7.CPCTC

Using the Parallel Postulate, draw m parallel to a.

2 & 3 are congruent (alt. int. s are ) 3 = 40°

4 & 5 are supplementary. 4 = 80°

1 = 40° + 80° = 120°

m4

3

2

5

PAI PAE PCA PSSIS PSSES 2P3P

Dual ̸̸̸̸ ̸̸ theorem Dual ⊥ theorem