3.4 Proving that Lines are Parallel Objectives: -Identify and use the converse of the Corresponding Angles Postulate. -Prove that lines are parallel by using theorems and postulates.. Warm-Up: Identify each angle.

Write the converse of the "Corresponding Angles Postulate." Postulate: If two lines cut by a transversal are parallel, then corresponding angles are congruent.

Theorem: Converse of the Corresponding Angles Postulate If two lines are cut by a transversal in such a way that corresponding angles are congruent, then the two lines are parallel. Converse of the Corresponding Angles Postulate: If corresponding angles are congruent, then the lines are parallel.

Converse of the Same Side Interior Angles Theorem If two lines are cut by a transversal in such a way that same side interior angles are supplementary, then the two lines are parallel. Theorem: Converse of the Same-Side Interior Angles Theorem: If same-side interior angles are supplementary, then the lines are parallel.

Converse of the Alternate Interior Angles Theorem If two lines are cut by a transversal in such a way that alternate interior angles are congruent, then the two lines are parallel. Theorem: Converse of the Alternate Interior Angles Theorem: If alternate interior angles are congruent, then the lines are parallel.

Converse of the Alternate Exterior Angles Theorem If two lines are cut by a transversal in such a way that alternate exterior angles are congruent, then the two lines are parallel. Theorem: Converse of the Alternate Exterior Angles Theorem: If alternate exterior angles are congruent, then the lines are parallel.

Theorem: If two coplanar lines are perpendicular to the same line, then the two lines are parallel to each other.

Theorem: If two coplanar lines are parallel to the same line, then the two lines are parallel to each other.

Are lines m & n parallel? Why or why not?

If m<1 = m<7, then 1 || 2 by the Converse of