In a ΔABC median AD is produced to x such that AD = DX. Prove that ABXC is a parallelogram.

Question:

In a ΔABC median AD is produced to x such that AD = DX. Prove that ABXC is a parallelogram.

Solution:

In a quadrilateral ABXC, we have

AD = DX [Given]

BD = DC [Given]

So, diagonals AX and BC bisect each other.

Therefore, ABXC is a parallelogram.

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