1. 5.2 Proving That Lines Are Parallel
Objective:
After studying this section, you will be able to apply the exterior angle inequality theorem and use various methods to prove lines are parallel.

2. An exterior angle of a triangle is formed whenever a side of the triangle is extended to form an angle supplementary to the adjacent interior angle. D
Exterior angle
Adjacent Interior angle F E
Remote Interior angle
Theorem 30: The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle.

3. (short form: Alt. int. lines.)
Theorem 31: If two lines are cut by a transversal such that two alternate interior angles are congruent, the lines are parallel.
(short form: Alt. int lines.)
Given: a
Prove: a ll b 3 b 6

4. (short form: Alt. ext. lines.)
Theorem 32: If two lines are cut by a transversal such that two alternate exterior angles are congruent, the lines are parallel.
(short form: Alt. ext lines.)
Given: a
Prove: a ll b 1 b 8

5. (short form: corr. lines.)
Theorem 33: If two lines are cut by a transversal such that two corresponding angles are congruent, the lines are parallel.
(short form: corr lines.)
Given: a 2
Prove: a ll b b 6

6. Theorem 34: If two lines are cut by a transversal
Theorem 34: If two lines are cut by a transversal such that two interior angles on the same side of the transversal are supplementary, the lines are parallel.
Given: a
Prove: a ll b 4 b 6

7. Theorem 35: If two lines are cut by a transversal
Theorem 35: If two lines are cut by a transversal such that two exterior angles on the same side of the transversal are supplementary, the lines are parallel.
Given: a 2
Prove: a ll b b 8

8. Theorem 36:If two coplanar lines are
Theorem 36:If two coplanar lines are perpendicular to a third line, they are parallel. a b
Given:
Prove: a ll b c

9. Given: a b
Prove: a ll b 1 2 c

10. Prove: MATH is a parallelogram
Given:
Prove: MATH is a parallelogram A T 3 1 2 4 H M

11. Prove: FROM is a TRAPEZOID
Given:
Prove: FROM is a TRAPEZOID
Note: A trapezoid is a four-sided figure with exactly one pair of parallel sides. S 3 O R 1 2 F M