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A B C D is a parallelogram. P is a point...

`A B C D` is a parallelogram. `P` is a point on `A D` such that `A P=1/3\ A D\ a n d\ Q` is a point on `B C` such that: `C Q=1/3B Cdot` Prove that `A Q C P` is a parallelogram.

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Solution
`ABCD` is a parallelogram.
`AD=BC` and `AD∥BC`.
`1/3 AD= 1/3 BC` 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.
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