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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=1/3A D` and `Q` is a point on `B C` such that `C Q=1/3B P` . Prove that `A Q C P` is a parallelogram.

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To Prove: `AQCP` is a parallelogram.
`ABCD` is a parallelogram.
`AD=BC` and `AD` parallel to `BC`
`1/3AD=1/3BC` and `AD` parallel to `BC`
`AP=CQ` and `AP` parllel to `CQ`
Thus, `AQCP` is a parallelogram such that one pair of opposite side `AP` and `CQ` are parallel and equal.
Hence, `AQCP` is a parallelogram.
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