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Prove that the line segment joining …

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Prove that the line segment joining the mid point of adjacent sides of aquadrilateral form a parallegram.

    • Posted by Rajesh Kumar Didwadiya 6 years, 9 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Gaurav Seth 6 years, 9 months ago

    Prove that the line segments joining the mid-points of the adjacent sides of a quadrilateral form a parallelogram

    GIVEN A quadrilateral ABCD in which P. Q, R and S are the mid-points of sides AB, BC, CD and DA respectively. TO PROVE PQRS is a parallelogram.

    CONSTRUCTION Join AC.
    PROOF In A ABC, P and Q are the mid-points of AB and BC respectively.

    PQ || AC

    In Δ ACD, R and S are the mid-points of CD and DA
    respectively.

    SR || AC

    From equations (i) and (ii), we have

    PQ II AC and SR || AC

    PQ || SR.

    Similarly, by considering triangles ABD and BCD, we can prove that PS || QR.

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