In a parallelogram $A B C D$ , $P$ is a point on side $A D$ such that $3 A P = A D$ and $Q$ is a point on $B C$ such that $3 C Q = B C$ . Prove that $A Q C P$ is a parallelogram.
If true answer is 1,else 0

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Solution

It is given that $A B C D$ is a parallelogram and since

$3 A P = A D$

$\Rightarrow$ $A P = \frac{1}{3} A D$

Also, it is given that

$3 C Q = B C$

$\Rightarrow$ $C Q = \frac{1}{3} B C$

Also since opposite sides of a parallelogram are equal, therefore, $A P = Q C$

Since $A B C D$ is a parallelogram, thus opposite sides are parallel, and therefore,

$A P ∥ Q C$

Also since one pair of opposite sides are equal and parallel, therefore, $A Q C P$ is a parallelogram.

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In a parallelogram ABCD, P is a point on side AD such that 3AP=AD and Q is a point on BC such that 3CQ=BC. Prove that AQCP is a parallelogram.If true answer is 1,else 0

In a parallelogram $A B C D$ , $P$ is a point on side $A D$ such that $3 A P = A D$ and $Q$ is a point on $B C$ such that $3 C Q = B C$ . Prove that $A Q C P$ is a parallelogram.
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