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-

ABCD is a parallelogram. AD=BC and AD∥ BC . 13AD=13BC and AD ∥ BC . AP=CQ and AP∥ CQ .Thus, APCQ is a parallelogram such that one ...

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Byju's Answer

Standard VIII

Mathematics

Elements of a Parallelogram

ABCD is a par...

Question

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

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Solution

ABCD is a parallelogram.
$A D = B C$ and $A D ∥ B C$ .
$\frac{1}{3} A D = \frac{1}{3} B C$ and $A D ∥ B C$ .

$A P = C Q$ and $A P ∥ C Q$ .
Thus, APCQ is a parallelogram such that one pair of opposite side AP and CQ are parallel and equal.
Hence, APCQ is a parallelogram.

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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.

ABCD is a parallelogram.AD=BC and AD∥BC.13AD=13BC and AD∥BC.AP=CQ and AP∥CQ.Thus, APCQ is a parallelogram such that one pair of opposite side AP and CQ are parallel and equal.Hence, APCQ is a parallelogram.

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

ABCD is a parallelogram.
$A D = B C$ and $A D ∥ B C$ .
$\frac{1}{3} A D = \frac{1}{3} B C$ and $A D ∥ B C$ .

$A P = C Q$ and $A P ∥ C Q$ .
Thus, APCQ is a parallelogram such that one pair of opposite side AP and CQ are parallel and equal.
Hence, APCQ is a parallelogram.