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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

Given : In ΔABC, AD is median and AD is produced to X such that DX = AD

To prove : ABXC is a parallelogram

Construction : Join BX and CX

Proof : In ΔABD and ΔCDX

AD= DX (Given)

BD = DC (D is mid points)

ADB=CDX (Vertically opposite angles)

ΔABDΔCDX (SAS criterian)

AB = CX (c.p.c.t)

and ABD=DCX

But these are alternate angles

AB||CX and AB=CX

ABXC is a parallelogram.


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