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 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.

\ ABC is an isosceles triangle with A B=A C . Side B A is produced to D such that A B=A D . Prove that /_B C D is a right angle.

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 Cdot Prove that A Q C P 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.

In a triangle A B C , if A B=A C\ a n d\ A B is produced to D such that B D=B C , find /_A C D\ :\ /_A D C

In Figure, A B C D is a parallelogram and X\ a n d\ Y are points on the diagonal B D such that D X=B Y . Prove that A X C Y is a parallelogram (ii) A X=C Y ,\ A Y=C X A Y B\ ~= C X D (iv) A X D~=\ C Y B

In Figure, A B C D is a parallelogram and X\ a n d\ Y are points on the diagonal B D such that D X=B Y . Prove that A X C Y is a parallelogram (ii) A X=C Y ,\ A Y=C X A Y B\ ~= C X D (iv) A X D~=\ C Y B

In Figure, A B C D is a parallelogram and X\ a n d\ Y are points on the diagonal B D such that D X=B Y . Prove that A X C Y is a parallelogram (ii) A X=C Y ,\ A Y=C X (iii) A Y B\ ~= C X D (iv) A X D~=\ C Y B

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.