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Transcript

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. Adjacent Interior angle E D Exterior angle F Remote Interior angle Theorem 30: The measure of an exterior angle of a triangle is greater than the measure of either remote interior angle. 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. s ll lines.) Given: 3 6 Prove: a ll b a 3 b 6 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.s ll lines.) Given: 1 8 Prove: a ll b a 1 b 8 Theorem 33: If two lines are cut by a transversal such that two corresponding angles are congruent, the lines are parallel. (short form: corr.s ll lines.) Given: 2 6 Prove: a ll b a 2 b 6 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: 4 supplement ary to 6 Prove: a ll b a 4 b 6 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: 2 supplement ary to 8 Prove: a ll b a 2 b 8 Theorem 36:If two coplanar lines are perpendicular to a third line, they are parallel. a b Given: a c and b c Prove: a ll b c Given: a c and b c a b Prove: a ll b 1 2 c Given: 1 2 MAT THM Prove: MATH is a parallelogram A 1 M T 3 4 2 H Given: 2 3 1 is supplement ary 3 Prove: FROM is a TRAPEZOID Note: A trapezoid is a four-sided figure with exactly one pair of parallel sides. S R F 2 3 O 1 M