In a parallelogram ABCD, points E and F are respectively midpoint of sides AB and CD (see the adjacent figure). Prove that line segment AF and EC trisect diagonal BD.

In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively. Show that the line segments AF and EC trisect the diagonal BD.

E and F are the mid-points of the sides AB and CD of a parallelogram ABCD. Prove that the line segment AF and CE trisects BD in three equal parts.

In a parallelogram ABCD, E and F are the mid-points of sides BC and AD respectively. Show that the line segment BF and ED trisect the diagonal AC.

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,ABCD is a parallelogram.E and F are the mid-points of the sides AB and CD respectively.Prov that the line segments AF and CE triset (divide into three equal parts) the diagonal BD.

Points E and F are respectively midpoints of sides AB and CD of a rectangle ABCD. If line segment AF and EC respectively intersect diagonal BD at P and Q, then what is the length of PQ if sides of rectangle are respectively 10 cm and 24 cm ?

ABCD is a parallelogram. L and M are respectively mid points of sides AB and DC. Prove that LD and MB trisects diagonals AC.

ABCD is a parallelogram with base AB = 12 cm and height 5 cm. If E and F are respectively midpoint of AB and CD and diagonal BD intersects AF and CE respectively at P and Q then area of quadrilateral PQCF is

In a parallelogram ABCD,points P and Q are points of trisection of diagonal BD.Prove that CQ is parallel to AP.

ABCD is a parallelogram in which P and Q are midpoints of opposite sides AB and CD respectively (see figure). If AQ intersects DP at S and BQ intersects CP at R, show that: (i) APCQ is a parallelogram.