Q. 84.0( 23 Votes )

ABCD is a paralle

Answer :

Given:- ABCD is parallelogram


BP=BD/3


DQ=BD/3


Formula used:- SAS congruency property


If 2 sides and angle between the two sides of both


the triangle are equal, then both triangle are congruent


Solution:-


In parallelogram ABCD


AO=OC and DO=OB [diagonal of parallelogram bisect each other]


As DO=OB


Where DO=DQ+OQ


OB=OP+PB


DQ+OQ=OP+PB


+OQ=OP+


OQ=OP+ -


OQ=OP


PQ = OP+OQ = 2(OQ) = 2(OP)


AC diagonal bisect PQ


In Δ QOC and Δ POA


OQ=PO [Proven above]


AO=OC [Diagonal of parallelogram bisect each other]


QOC= AOP [vertically opposite angles]


Hence Δ QOC Δ POA


CQO= OPA


If QC and PA are 2 lines


And QP is the transverse


And CQO= OPA by Alternate angles


QC||PA


Conclusion:-


CQ||PA and CA is bisector of PQ.


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