`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 .

In Fig. A B C is right angled at C and D E_|_A B . Prove that A B C∼A D E and hence find the length of AE and DE

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. 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=

In /_\A B C ,D is the mid-point of BC and ED is the bisector of the /_ADB and EF is drawn parallel to B C cutting A C in F . Prove that /_E D F is a right angle.

A B C D is a parallelogram, G is the point on A B such that A G=2\ G B ,\ E\ is a point of D C such that C E=2D E\ a n d\ F is the point of B C such that B F=2F C . Prove that: a r\ (triangle \ E F C)=1/2\ a r\ (triangle \ E B F)

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.