`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 in which B C is produced to E such that C E=B CdotA E intersects C D\ at Fdot 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 ^(gm) ABCD

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 cyclic quadrilateral. A Ba n dD C are produced to meet in Edot Prove that E B C-E D Adot

In Figure, A B C D is a parallelogram in which P is the mid-point of D C and Q is a point on A C such that C Q=1/4A Cdot If P Q produced meets B C at Rdot Prove that R is a mid-point of B Cdot

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.

A B C D is a parallelogram, G is the point on A B such that A G=2G B ,E is a point of D C such that C E=2D E and F is the point of B C such that B F=2F Cdot Prove that : a r(A D E G)=a r(G B C E) a r( E G B)=1/6a r(A B C D)

P is the mid-point of side A B of a parallelogram A B C D . A line through B parallel to P D meets D C at Q\ a n d\ A D produced at Rdot Prove that: A R=2B C (ii) B R=2\ B Q

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 Fdot Then A F= 3/2A B (b) 2\ A B (c) 3\ A B (c) 5/4\ A B

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 is a triangle. D is a point on A B such that D=1/4A B\ a n d\ E is a point on A C such that A E=1/4A Cdot Prove that D E=1/4B C