Question

If a transversal intersects two lines such that a pair of alternate interior angles is equal then the two lines are parallel

prove it with figure

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Answer 1

Hence Proved.

Hope this help you

Answer 2

Given

• A Transversal r intersect 2 lines AB and CD , at P and Q respectively.

• Such that Angle 1 and Angle 2 are pairs of alternate intersect angles and

• Angle 1 = Angle 2

To prove

AB || CD

Proof

Here we can say ,

Angle 2 = Angle 3 as they are vertically opposite angles .

Angle 1 = Angle 2 ( given )

So here left with Angle 1 Angle 3 to be equal

Angle 1 = Angle 3 ( Corresponding Angles )

when corresponding pairs are equal that means line are parallel so ,

Using Corresponding Angles Axi om =

AB || CD

AB || CDTherefore, we Proved AB || CD