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Example 5 - If a transversal intersects two lines such that - Parallel lines and traversal - Problems

Example 5 - Chapter 6 Class 9 Lines and Angles - Part 2

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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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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.