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16. In the adjoining figure, P is the mid-point of the side BC of a
parallelogram ABCD such that <BAP = <DAP. Prove that AD = 2CD.
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Given : P is the mid-point of the side BC of a parallelogram ABCD
∠BAP = ∠DAP
To Find : Prove that AD = 2CD.
Solution:
Draw a line PQ || AB Q is point on AD
=> ∠QAP = ∠DAP
∠BAP = ∠DAP
=> ∠BAP = ∠QAP
∠QAP = ∠BPA ( alternate angle as AQ || PB ∵ AD || BC)
∠BAP = ∠BPA
=> AB = BP
P is mid point of BC
=> BC = 2BP
BC = AD
=> AD = 2BP
=> AD = 2AB
AB = CD
=> AD = 2CD
QED
Hence proved
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