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Locus of the Points Equidistant From Two Intersecting Lines

In parallelog...

Question

In parallelogram ABCD, O is any point on diagonal AC. Prove that ar(OBC)=ar(OCD).

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Q. P is any point on the diagonal AC of a parallelogram ABCD. Prove that ar(∆ADP) = ar(∆ABP).

$O$ is any point on the diagonal $P R$ of parallelogram $P Q R S$ .

Prove that $a r (△ P S O) = a r (△ P Q O)$ .

Q. P is any point on the diagonal BD of the parallelogram ABCD. Prove that

Δ A P D = Δ C P D

Q. In the adjoining figure, ABCD is a parallelogram and O is any point on the diagonal AC. Show that ar(∆AOB) = ar(∆AOD).

M

N

are taken on the diagonal

A C

of a parallelogram

A B C D

A M = C N

B M D N

is a parallelogram.

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