In a triangle ABC, median AD is produced to X such that AD = DX. Prove that ABXC is a parallelogram. [2 MARKS]

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Solution

Concept : 1 Mark
Proof : 1 Mark

Since AD is the median, it bisects the side BC.

Hence, BD = DC.

Also given that X is defined such that AD = DX.

Hence, the diagonals AX and BC of a quadrilateral ABXC bisect each other.

We know that in a paralellogram, the diagonals bisect each other.

$∴$ ABXC is a parallelogram

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

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

Assertion : In $Δ A B C$ , median AD is produced to X such that AD = DX. Then, ABXC is a parallelogram.
Reason : Diagonals AX and BC bisect each other at right angles.
Which of the following is correct?

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