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Prove that the parallelogram between the …

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Prove that the parallelogram between the same base and the same parallel lines is equal in area.

    • Posted by Moeen Ahmed 5 years, 4 months ago

    CBSE > Class 09 > Mathematics
    • 1 answers

    Gaurav Seth 5 years, 4 months ago

     

    Let ABCD and EFCD be two parallelograms lying on the same base CD and between the same parallels AF and CD.

    We have to prove that area of the parallelograms ABCD and EFCD are equal.

    In ADE and BCF,

    DAE = CBF (Corresponding angles)

    AED = BFC (Corresponding angles)

    AD = BC (Opposite sides of the parallelogram ABCD)

     ADE  BCF (By ASA congruence rule)

     

    We know that congruent figures have the same area.

     area (ADE) = area (BCF) … (1)

     

    Now, we have:

    area (ABCD) = area(ADE) + area (EDCB)

    = area (BCF) + area (EDCB) [Using (1)]

    = area (EDCF)

    Thus, the areas of the two parallelograms ABCD and EFCD are the same.

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