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In a A B C median A D is produced to X ...

In a ` A B C` median `A D` is produced to `X` such that `A D=D X` . Prove that `A B X C` is a parallelogram.

Text Solution

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In `DeltaABC,` since D is the mid-point of BC
`{:(therefore,AD=DC),(and,AD=DX):}`
Now, in quadrilateral ABXC,
AD=DX and BD = DC
i.e., its diagonals bisect each other.
Therefore, `squareABXC` is a parallelogram.
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