The quadrilateral $ABCD$ has two parallel sides. Let $M$ and $N$ be the midpoints of $[DC]$ and $[BC]$, and $P$ the common point of the lines $AM$ and $DN$. If $\frac{PM}{AP}=\frac{1}{4}$, prove that $ABCD$ is a parallelogram.
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Tags: geometry, parallelogram
The quadrilateral $ABCD$ has two parallel sides. Let $M$ and $N$ be the midpoints of $[DC]$ and $[BC]$, and $P$ the common point of the lines $AM$ and $DN$. If $\frac{PM}{AP}=\frac{1}{4}$, prove that $ABCD$ is a parallelogram.