Question

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

Answer 1

Given that $AD=DX$

Also $BD=DC$ (because of median bisector that side of $△$ )

This show that diagonal $AX$ and $BC$ of $△AB\times C$ bisect each other at $D$ which is property of $11gram$

Thus $AB\times C$ is a parallelogram