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,

Therefore,

AQCP is a parallelogram

Proved!

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1s2, 2s2, 2p6, 3s2, 3p6, 4s2, 3d10, 4p6, 5s2, 4d10, 5p2

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