Question

Prove if a transversal intersect two Parallel Lines then each pair of alternate interior angles is equal

Answer 1

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here is your answer...

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GIVEN :-
The transversal PS intersects line AB and CD at points Q and R respectively such that angle PQR is equal to angle QRC.

TO PROVE :-
AB || CD

PROOF :-
angle BQR = angle PQA ( vertically opposite angles ) ..... equation 1
But, angle BQR = angle QRC ..... equation 2
Now, from equation 1 and 2, we get,
angle PQA = angle QRC
but they are corresponding angles
So, AB || CD ( by converse of corresponding angles axiom)

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