Question

Q.
Prove that, if a transversal intersects two lines, such that pair of alternate interior angles is equal, then the two lines are
parallel
​

Answer 1

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= 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.

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