Question

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

Answer 1

consd.r tri.'sABX & QCX.here,
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