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ABCD is a parallelogram E and F are mid points of the sides AB and CD respectively AF and DE intersects at P BF and CE intersects at Q prove that AECF is a parallelogram |
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Answer» Step-by-step EXPLANATION: ABCD is ∥gm AB∥CD AE∥FC ⇒AB=CD
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CD AE=EC AECF is ∥gm In △DQC F is mid point of DC FP∥CQ By CONVERSE of mid point theorem P is mid point of DQ ⇒DP=PQ (1) ∴AF and EC bisect BD In △APB E is mid point of AB EQ∥AP By converse of MPT ( mid point theorem ) Q is mid point of PB ⇒PQ=QB (2) By (1) and (2) ⇒PQ=QB=DP AF and EC bisect BD.. |
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