ABCD is a parallelogram,P and Q are points on DC and AB respectively,such that angle DAP=angleBCQ.Show that Acqp is a parallelogram.

Given: A parallelogram ABCDTo Prove: APCQ is parallelogram.Proof: A = C{Opposite angle of parallelogram are equal}DAP +PAQ = PCQ+QCBPAQ = PCQ Which is a pair of opposite anglesso, APCQ is parallelogram.

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It is given that angDAP= angBCQ.

But angDAP= ang APC ( alternate interior angles) and

angBCQ= ang AQC (alternate interior angles)

Therefore angAPC= ang AQC

Consider Quadrilateral AQCP,

Opposite angles i.e. ang APC and ang AQC are equal,


AQCP is a parallelogram


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