Math 109

Section 2.3

Proving Lines Parallel

Converses of the theorems in chapter 2

Theorem 2.3.1: If two lines are cut by a transversal so that the corresponding angles are congruent, then the lines are parallel.

Theorem 2.3.2: If two lines are cut by a transversal so that the alternate interior angles are congruent, then the lines are parallel.

Theorem 2.3.3: If two lines are cut by a transversal so that the alternate exterior angles are congruent, then the lines are parallel.

Theorem 2.3.4: If two lines are cut by a transversal so that the interior angles on the same side of the transversal are supplementary, then the lines are parallel.

Theorem 2.3.5: If two lines are cut by a transversal so that the exterior angles on the same side of the transversal are supplementary, then the lines are parallel.

Theorem 2.3.6: If two lines are parallel to a third line, then these lines are parallel to each other.

Theorem 2.3.7: If two coplanar lines are perpendicular to a third line, then they are parallel to each other.

Examples Section 2.3

Use to answer #1-6

Determine if lines and are parallel on the basis of the given information.

2) are alternate interior angles.

4)

6)

8)

10)

12) by theorem 2.3.6

14) are supplementary angles