Warm-Up

x + 2

3x - 6

What is the value of x?

Geometry 3-3

Proving Lines Parallel

Use the Converse of the Corresponding Angles Postulate and the given information to show that ℓ || m.

Example: Using the Converse of the Corresponding Angles Postulate

m3 = (4x – 80)°, m7 = (3x – 50)°, x = 30

• Converse of the Alternate Interior Angle Theorem:

If two alternate interior angles are congruent, then the lines are parallel.

• Converse of the Alternate Exterior Angle Theorem:

If two alternate exterior angles are congruent, then the lines are parallel.

• Converse of the Same Side Interior Angle Theorem:

If two same side interior angles sum up to 180°, then the lines are parallel.

m2 = (10x + 8)°, m3 = (25x – 3)°, x = 5

Show that r || s.

Example 2: Determining Whether Lines are Parallel