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.

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.

(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

(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

(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

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

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

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

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

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

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