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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Similar questions

Q. In a triangle

A B C

median

A D

is produced to

X

such that

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. Prove that

A B X C

is a parallelogram.

In a $Δ A B C$ median AD is produced to X such that AD = DX. Prove that ABXC is a parallelogram.

In a triangle ABC, 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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Δ A B C

, AD is the median through A and E is the midpoint of AD. BE produced meets AC in F such that BF DK. Prove that

A F = \frac{1}{3} A C

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