Question

in parallelogram ABCD, P and q are points on side ab and cd, such that AP=QC. prove that diagonal AC and PQ bisect each other.​

Answer 1

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Let point of intersection of AC and PQ be E.
Taking triangle AEP and CEQ.
AP = CQ (given)
angle EAP = angle ECQ (alternate interior angles are always equal)
angle EPA = angle EQC (alt. int. angles).
So, by ASA triangle AEP is congruent to triangle CEQ.
By c.p.c.t.c, AE =EC and PE = EQ

Answer 2

Answer:

Let point of intersection of AC and PQ be E.

Taking triangle AEP and CEQ.

AP = CQ (given)

angle EAP = angle ECQ (alternate interior angles are always equal)

angle EPA = angle EQC (alt. int. angles).

So, by ASA triangle AEP is congruent to triangle CEQ.

By c.p.c.t.c, AE =EC and PE = EQ

Step-by-step explanation:

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