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# Proof proof

In the given figure ABCD is a parllelogram.

Prove that ar(BCP)= ar(DPQ) if BC=CQ.

Note by Vishwathiga Jayasankar
9 months, 2 weeks ago

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$$CP \parallel AB, BC = CQ \Rightarrow AP = PQ$$ (midpoint theorem).
Considering congruences, we get $$CP = PD$$.
Then $$[ADP] = [BPC] = [CPQ] = [DPQ]$$ by properties of the median, considering parallel lines and common bases. · 9 months, 2 weeks ago