`A B C D` is a parallelogram and `E\ a n d\ F` are the centroids of triangles `A B D\ a n d\ B C D` respectively, then `E F=`
(a)`A E`
(b) `B E`
(c) `C E`
(d) `D E`

In Figure, A B C D is a parallelogram. E\ a n d\ F are the mid-points of the sides A B\ a n d\ C D respectively. Prove that the line segments A F\ a n d\ C E trisect (divide into three equal parts) the diagonal B D .

A B C D is a parallelogram, E\ a n d\ F are the mid-points of A B\ a n d\ C D respectively. G H is any line intersecting A D ,\ E F\ a n d\ B C at G ,\ P\ a n d\ H respectively. Prove that G P=P H

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 a parallelogram A B C D ,E ,F are any two points on the sides A B and B C respectively. Show that a r( /_\A D F)=a r( /_\D C E).

In a parallelogram A B C D ,E ,F are any two points on the sides A B and B C respectively. Show that a r(triangle A D F)=a r( triangle D C E) .

A B C D is a square E ,\ F ,\ G\ a n d\ H are points on A B ,\ B C ,\ C D\ a n d\ D A respectively, such that A E=B F=C G=D H . Prove that E F G H is square.

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 trapezium with parallel sides A B=a\ a n d\ D C=bdot If E\ a n d\ F are mid-points of non-parallel sides A D\ a n d\ B C respectively, then the ratio of areas of quadrilaterals A B F E\ a n d\ E F C D is: a : b (b) (a+3b):(3a+b) (3a+b):(a+3b) (d) (3a+b):(3a+b)

A B C D is a square E ,\ F ,\ G\ a n d\ H are points on A B ,\ B C ,\ C D\ a n d\ D A respectively, such that A E=B F=C G=D Hdot Prove that E F G H is square.

A D\ a n d\ B E are respectively altitudes of A B C such that A E=B D . Prove that A D=B E .