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.​

Answer 1

Answer:

Here is ur ans.

Step-by-step explanation:

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....

Plz mark as brain list....

Answer 2

Answer:

Check your answer please