`A B C D` is a parallelogram. `E ,F` are mid-points of `B C ,C D` respectively. `A E ,A F` meet the diagonal `B D` at points Q and P respectively. Show that points P and Q trisect DB`.

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 D is a parallelogram. E and F are the mid-points of the sides A B and C D respectively. Prove that the line segments A F and C E triset (divide into three equal parts) the diagonal B Ddot

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

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 .

In Figure, A B C D is a parallelogram and X ,Y are the mid-points of sides A B and D C respectively. Show that A X C Y is a parallelogram.

D, E and F are the mid-points of the sides AB, BC and CA respectively of A ABC. AE meets DF at O. P and Q are the mid-points of OB and OC respectively. Prove that DPOF is a parallelogram.

In Figure, A B C D is a parallelogram and X ,Y are the mid=points of sides A B and D C respectively. Show that A X C Y is a parallelogram. Figure

Prove that the figure formed by joining the mid-points of the pair of consecutive sides of a quadrilateral is a parallelogram. OR ABC D is a parallelogram in which P ,Q ,R and S are mid-points of the sides A B ,B C ,C D and D A respectively. A C is a diagonal. Show that : P Q|| A C and P Q=1/2A C S R || A C and S R=1/2A C P Q=S R (iv) P Q R S is a parallelogram.

In A B C ,\ D and E are the mid-points of A B and A C respectively. Find the ratio of the areas of A D E and A B C .

A B C D is a rhombus and P ,\ Q ,\ R ,\ S are the mid-points of A B ,\ B C ,\ C D ,\ D A respectively. Prove that P Q R S is a rectangle.