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In a triangle A B C median A D is produc...

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

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In quadrilateral ABXC, we have
`AD=DX`(Given
`BD=DC`(Given)
So, diagonals `AX \and\ BC` bisect each other.
Therefore,`ABXC` is a parallelogram.
`/_BDA=/_CDX`
`/_\ABD~~/_\XCD`
`XC=AB`
`/_ABC=/_XCB`
These two angles form a pair of alternate angles.
`AB∣∣CX`
Now, as two opposite sides are parallel and equal, we can say that `ABXC` is a parallelogram.
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