# <span lang="EN-US

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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