MathematicsP is the mid-point of side BC of a parallelogram ABCD such that ∠BAP =∠DAP. If AD =10 cm, then the measure of CD is ____ cm.

P is the mid-point of side BC of a parallelogram ABCD such that ∠BAP =∠DAP. If AD =10 cm, then the measure of CD is ____ cm.


In the below figure, P is the mid - point of side BC of a parallelogram ABCD such that BAP = DAP . Prove that AD = 2CD

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    Solution:

    P is the mid-point of side BC of a parallelogram ABCD such that ∠BAP =∠DAP. If AD =10 cm, then the measure of CD is 5 cm.
    Given P is the mid-point of side BC of a parallelogram ABCD such that ∠BAP =∠DAP.
    Now, the sides opposite to equal angles are equal.
    AB=BP BP= 1 2 BC   ⇒ AB= 1 2 BC   Therefore,
    AD=BC=10cm   Now,
    AB= 1 2 (10cm)   ⇒ AB=5cm   Now, as ABCD is a parallelogram, the opposite sides are equal and parallel.
    CD = AB = 5 cm.
    Hence, the measure of CD is 5 cm.
     
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