Lesson 2-5: Proving Lines Parallel 1

Lesson 3 - 5

Proving Lines Parallel

Lesson 2-5: Proving Lines Parallel 2

Proving Lines Parallel - Postulates & Theorems

If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.

DC

BA

Lesson 2-5: Proving Lines Parallel 3

Proving Lines Parallel - Postulates &Theorems

If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel.

DC

BA

Lesson 2-5: Proving Lines Parallel 4

Proving Lines Parallel - Postulates &Theorems

If two lines are cut by a transversal and consecutive interior angles are supplementary, then the lines are parallel.

DC

BA

Lesson 2-5: Proving Lines Parallel 5

Proving Lines Parallel - Postulates &Theorems

If two lines are cut by a transversal and consecutive exterior angles are supplementary, then the lines are parallel.

DC

BA

Lesson 2-5: Proving Lines Parallel 6

Examples: Proving Lines Parallel

Find the value of x which will make lines a and lines b parallel.

4. 20°Answers: 1. 20° 2. 50° 3. 45°

2.

80

2x

b

a1.

60

3x

b

a

3.

70

(x-20)

b

a 4.

60

3x

b

a

Lesson 2-5: Proving Lines Parallel 7

Ways to Prove Two Lines Parallel

Show that corresponding angles are equal. Show that alternative interior angles are equal. Show that consecutive interior angles are

supplementary. Show that consecutive exterior angles are

supplementary. In a plane, show that the lines are perpendicular to the

same line.