# ABCD is a paralle

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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ABCD is a paralleAP- Mathematics

ABCD is a paralleAP- Mathematics