Question

If a transversal intersects two line such that the bisectors of corresponding angels are parallel,then prove that the tow line are parallel ​

Answer 1

The transversal AD intersects the two lines PQ and RS at points B and C respectively. BE is the bisector of ∠ABQ and CF is the bisector of ∠BCS.

As, BE is the bisector of ∠ABQ, then,

∠ABE= 2/1∠ABQ

In the same way,

∠BCF= 2/1 ∠BCS

Since BE and CF are parallel and AD is the transversal, therefore, by corresponding angle axiom,

∠ABE=∠BCF

2/1∠ABQ= 2/1∠BCS

∠ABQ=∠BCS

Therefore, by the converse of corresponding angle axiom,

PQ∥RS.