Question

if transversal intersects two lines such that bisectors of a pair of corresponding angles are parallel then prove that two lines are parallel​

Answer 1

Answer:

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=1/2 ∠ABQ

In the same way,

∠BCF=1/2 ∠BCS

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

∠ABE=∠BCF

1/2 ∠ABQ=1/2 ∠BCS

∠ABQ=∠BCS

Therefore, by the converse of corresponding angle axiom,

PQ∥RS.