Question

6. Pand Q are the points of trisection of the diagonal BD of a parallelogram ABCD. Prove
that is parallel to AP. Prove also that AC bisects PQ.
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Answer 1

$\large{\underbrace{\sf{\green{Correct\:Question:}}}}$

• P and Q are the points of trisection of the diagonal BD of a parallelogram ABCD. Prove that CQ is parallel to AP. Prove also that AC bisects PQ.

$\large{\underline{\sf{\red{Solution:}}}}$

We know that,

Diagonals of a parallelogram bisect each other,

→ $\rm{OA=OC \:and\:OB=OD}$

Since P and Q are points of trisection of BD,

$\rm{\therefore\:BP=PQ=QD}$

Now,

• OB = OD

• BP = QD

→ $\rm{OB - BP = OD - QD }$

→ $\rm{ OP=OQ }$

Now, In quadrilateral APCQ

We have

• OA=OC

• OP=OQ

→ Diagonals of quadrilateral APCQ bisect each other.

→ APCQ is a parallelogram.

Hence,

→ $\rm{AP \parallel CQ}$

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