Answer :

Given: ABCD is a quadrilateral in which ABDC and BP = PC


To prove: AB=CQ and DQ=DC+AB


Proof:


In ∆ABP and ∆PCQ we have,


PAB = PQC …alternate angles


APB = CPQ … vertically opposite angles


BP = PC … given


Thus by AAS property of congruence,


∆ABP PCQ


Hence, we know that, corresponding parts of the congruent triangles are equal


AB = CQ …(1)


But, DQ = DC + CQ


= DC + AB …from 1


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