Question

Prove if a transversal intersects two parallel lines then each pair of interior angles is equal.

Answer 1

To Prove :

Angle 3 = Angle 2

Angle 5 = Angle 4

Proof : .
Angle 1 = Angle 3 ( Vertical opposite angles)

Angle 1 = Angle 2 (Corrosponding Angles)

=> Angle 2 = Angle 3 -(1)

Angle 6 = Angle 5 (Vertical opposite angles)

Angle 6 = Angle 4 (Corrosponding Angles)

=> Angle 5 = Angle 4 -(2)

In (1)&(2) we have proved.

Answer 2

Solution :

Given : Two parallel lines AB and CD

Let PS be the transversal AB at Q and CD at R.

To prove : Each pair of alternate interior angles are equal.

So, ∠BQR = ∠CRQ

And, ∠AQR = ∠QRD

Proof : As we have to prove that ∠BQR = ∠CRQ

For lines AB and CD, they are parallel and with transversal PS.

∠AQP = ∠CRQ ( corresponding angles )...(i)

And, ∠AQP = ∠BQR ( vertically opp.).....(ii)

From ( i ) and ( ii )

∠ BQR = ∠CRQ

Similarly, we can prove

∠AQR = ∠QRD

Hence, pair of alternate interior angles are equal.

Hence it is proved.