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Question

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

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Solution

is given with AD as the median extended to point X such that .

Join BX and CX.

We get a quadrilateral ABXC, we need to prove that it’s a parallelogram.

We know that AD is the median.

By definition of median we get:

Also, it is given that

Thus, the diagonals of the quadrilateral ABCX bisect each other.

Therefore, quadrilateral ABXC is a parallelogram.

Hence proved.


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