In ` A B C ,A D` is the median through `A` and `E` is the mid-point of `A D` . `B E` produced meets `A C` in `F` (Figure). Prove that `A F=1/3A 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=

In Figure, A B C\ a n d\ B D E are two equilateral triangls such that D is the mid-point of B C. If A E intersects B C in F , Prove that: a r( B D E)=1/4a r\ (\ A B C) .

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. 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

In Figure, A B C\ a n d\ B D E are two equilateral triangls such that D is the mid-point of B CdotA E intersects B C in Fdot Prove that: a r\ (\ B F E)=\ a r\ (\ A F D)

In Figure, A D\ a n d\ B E are medians of A B C\ a n d\ B E||D F . Prove that C F=1/4A C .

A B C is a triangle in which D is the mid-point of BC and E is the mid-point of A D . Prove that area of triangle B E D=1/4area \ of triangle A B C . GIVEN : A triangle A B C ,D is the mid-point of B C and E is the mid-point of the median A D . TO PROVE : a r( triangle B E D)=1/4a r(triangle A B C)dot

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

In a A B C ,\ E\ a n d\ F are the mid-points of A C\ a n d\ A B respectively. The altitude A P to B C intersects F E\ at Q . Prove that A Q=Q P .