Question

if a transversal intersects two lines such that the bisectors of a pair of alternate interior angles are parallel , then prove that the two lines are parallel.


plz tell correct answer . and if you don't know the answer plz don't text sorry or i don't know​

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=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.