# ABCD is a parallelogram and X is mid point ofBC .THE line AX produced meets DC produced at Q.the parallelogram AQPB IS completed ,Prove that triangle ABX is congruent to triangleQCX and DC=CQ=QP

1
by hafzajamal28

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by hafzajamal28

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BX=CX

ABX=XCQ(alt int ang)

AXB=CXQ(VERT.OPP.ANG.)

therefore they are congrunt by ASA

i.e

ab=cq (CPCT)_

&

AB=DC (opp sides of llgm)

&

CQ=BP ( ' ')

=>AB=CQ=DC=BP