Question

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

Answer 1

Answer:here is ur answer hope it helps you

Step-by-step explanation:

Answer 2

Answer:

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

and BE||CG.

We have to prove that PQ || RS

It is given that ray BE is the bisector of ∠ ABQ.

Therefore , ∠ABE=  1/2  ∠ABQ                             (1)

Similarly , ray CG is the bisector of ∠ BCS

Therefore , ∠BCG =  1/2 ∠BCS                            (2)

But BE || CG and AD is the transversal .

Therefore ,   ∠ABE = ∠BCG

                          ( corresponding angles axiom)   (3)

Substituting (1) and (2) in (3), you get

                  1/2 ∠ ABQ = 1/2 ∠ BCS

That is , ∠ ABQ = ∠ BCS

But , they are the corresponding angles formed by the transversal AD with PQ and RS; and are equal.

Therefore,      PQ || RS

                           (converse of corresponding angles axiom)

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