In a ΔABC median AD is produced to X such that AD = DX. Prove that ABXC is a parallelogram.
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)
∴ΔABD≅ΔCDX (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.