Question

P is the mid-point of BD. ZABP = ZDCP and ZDPB = ZAPC. Prove that AB = CD.
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Answer 1

Given :

AB//DC ,and P is the midpoint of BD.

To prove : P is the midpoint of AC

Or

[ PA = PC ]

Proof :

In ∆PDC and ∆PBA ,

<PDC = <PBA

[ AB//DC, alternate angles ]

PD = PB [ P is the midpoint of BD ]

<DPC = <BPA [ Vertically opposite angles]

Therefore,

∆PDC is congruent to ∆PBA

Now ,

PC = PA [ C.P.C.T ]

P is the midpoint of AC