Two segments `A C` and `B D` bisect each other at `O` . Prove that `A B C D` is a parallelogram.

Two segments AC and BD bisect each other at O. Prove that ABCD is a parallelogram.

The sides A B and C D of a parallelogram A B C D are bisected at Ea n dF . Prove that E B F D is a parallelogram.

In a A B C median A D is produced to X such that A D=D X . Prove that A B X C is a parallelogram.

In a A B C median A D is produced to X such that A D=D X . Prove that A B X C is a parallelogram.

The sides A B\ a n d\ C D of a parallelogram A B C D are bisected at E\ a n d\ F . Prove that E B F D is a parallelogram.

In a triangle A B C median A D is produced to X such that A D=D Xdot Prove that A B X C is a parallelogram.

In a triangle A B C median A D is produced to X such that A D=D Xdot Prove that A B X C is a parallelogram.

In a triangle A B C median A D is produced to X such that A D=D Xdot Prove that A B X C is a parallelogram.

The sides A B\ a n d\ C D of a parallelogram A B C D are bisected at E\ a n d\ Fdot Prove that E B F D is a parallelogram.

A B C D is a parallelogram. P is a point on A D such that A P=1/3\ A D\ a n d\ Q is a point on B C such that C Q=1/3B C . Prove that A Q C P is a parallelogram.