Question

If a transversal intersects two lines such that the bisectors of a pair of corresponding angles are parallel, then
prove that the two lines are also parallel.
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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.

Step-by-step explanation:

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