`A B C D` is a rhombus, `E A B F` is a straight line such that `E A=A B=B F` . Prove that `E D` and `F C` when produced meet at right angles.

A B C D is a parallelogram. If A B is produced to E such that B E=A B . Prove that E D bisects B C .

A B C D is a parallelogram and E is the mid-point of B C ,\ D E\ a n d\ A B when produced meet at F . Then A F=

A B C D is a parallelogram. A D is a produced to E so that D E=D C and E C produced meets A B produced in Fdot Prove that B F=B Cdot

A B C D is a parallelogram. A D is a produced to E so that D E=D C and E C produced meets A B produced in Fdot Prove that B F=B Cdot

A B C D is a parallelogram. A D is a produced to E so that D E=D C and E C produced meets A B produced in Fdot Prove that B F=B Cdot

A B C D is a parallelogram. E is a point on B A such that B E=2\ E A\ a n d\ F is a point on D C such that D F=2\ F C . Prove that A E C F is a parallelogram whose area is one third of the area of parallelogram A B C D .

If A B C and D E F are similar triangles such that 2\ A B=D E and B C=8c m , then E F=

A B C D is a parallelogram. E is a point on B A such that B E=2\ E A\ a n d\ F is a point on D C such that D F=2\ F Cdot Prove that A E\ C F is a parallelogram whose area is one third of the area of parallelogram A B\ C Ddot

A B C D is a parallelogram in which B C is produced to E such that C E=B C. A E intersects C D\ at F . Prove that a r\ (\ A D F)=\ a r\ (\ E C F) . If the area of \ D F B=3\ c m^2, find the area of ABCD.

If A B C\ a n d\ D E F are two triangles such that A B ,\ B C are respectively equal and parallel to D E ,\ E F , then show that Quadrilateral A B E D is a parallelogram Quadrilateral B C F E is a parallelogram A C=D F (iv) A B C\ ~=\ D E F