Last updated at Dec. 8, 2016 by Teachoo
Example 5 If a transversal intersects two lines such that the bisectors of a pair of corresponding angles are parallel, then prove that the two lines are parallel. In figure, transversal AD intersects two lines PQ and RS at points B and C respectively. Ray BE is the bisector of ∠ BACQ So , ∠ ABE = ∠ EBQ = 1/2(∠ ABQ ) and ray CG is the bisector of ∠ BCS; So , ∠ BCG = ∠ GCS = 1/2(∠BCS) and BE || CG. We have to prove PQ || RS Since BE || CG, & line AD is a transversal ∠ ABE = ∠ BCG 1/2(∠ ABQ )= 1/2 (∠ BCS) ∠ ABQ= ∠ BCS But, these angles are the corresponding angles formed by transversal AD with PQ and RS From Axiom 6.4: If a transversal intersects two lines such that pair of corresponding angles is equal, then lines are parallel to each other So, PQ || RS Hence proved.
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