Question

Heya !!

Prove the theorem - 6.2

If a transversal intersects two Parallel Lines then each pair of alternate interior angles is equal.


Help needed !! Thank you in advance.

Answer 1

Theorem 6.2:

If a transversal intersects two parallel lines then each pair of alternate interior angles is equal.

To Prove :

Alternate Interior Angles are equal.

For solution refer to the above attachment !!

Answer 2

Refer the attachment for figure


To prove :- angle BQR = angle CRQ (alternate interior angles are equal)

We will use the theorem that :-

Corresponding angles are equal and
Vertically opposite angles are equal.

So, in the figure,

angle AQP = angle CRQ (corresponding angles)

angle AQP = angle BQR (vertically opposite angles)

Hence, angle BQR = angle CRQ

(Things which are equal to the same things are equal to each other)

Hence, Alternate interior angles are equal