ABCD is a parallelogram-p is apoint on AD such that AP-1-3 AD and Q IS A POINT ON BC such that CQ-1-3 BC-PROVE THAT AQCP IS A PARALLELOGRAM

GIVEN ABCD is a parallelogram AP= 1/3 AD and CQ = 1/3BC AD = BC( opp. sides of a IIgm are equal) 1/3AD = 1/3BC i.e AP = CQ ( given that AP= 1/3 AD and CQ = 1/3B ...

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Standard IX

Mathematics

Properties of Parallelogram

ABCD is a par...

Question

$A B C D$ is a parallelogram. $P$ is a point on $A D$ such that $A P = \frac{1}{3} A D$ and Q is a point on $B C$ such that $C Q = \frac{1}{3} B C$ . Prove that $A Q C P$ is a parallelogram.

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Solution

Given: $A B C D$ is a parallelogram
$A P = \frac{1}{3} A D$ and $C Q = \frac{1}{3} B C$
$A D = B C$ ( opp. sides of a parallelogram are equal)
$\frac{1}{3} A D = \frac{1}{3} B C$ i.e $A P = C Q$ ( given that $A P = \frac{1}{3} A D$ and $C Q = \frac{1}{3} B C$ )
$A D ∥ B C$ ( opp. side of a parallelogram are II )
So, $A P ∥ C Q$
So $A P C Q$ is a parallelogram ( one pair of opp. sides are equal and parallel)

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ABCD is a parallelogram. P is a point on AD such that AP=13AD and Q is a point on BC such that CQ=13BC. Prove that AQCP is a parallelogram.

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