E is the mid-point of the side BC of the parallelogram ABCD. DE and extended AB intersects each other at F. If AB = 4 cm, then AF =

D, E and F are the mid-points of the sides AB, AC and BC of the DeltaABC. Prove that DE and AF bisects each other.

E is the mid-point of the side AD of the trapezium ABCD with AB||DC . A line through E drawn parallel to AB intersects BC at F. then

If E is a point on side AD produced of a parallelogram ABCD and BE intersects CD at F , Prove that /_\ABE~/_\CFB .

E is the mid-point of the side AD of the tarapezium ABCD with AB||DC . A line through E drawn parallel to AB intersects BC at F. Show that F is the mid-points of BC.

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.

The bisectors of angleA and angleB meet at a point E on the side CD of the parallelogram ABCD . If the length of the side BC be 2 cm , find the length of the side AB.

The side AD of parallelogram ABCD is produced to a point E. BE intersects CD at F. Show that Delta ABE~ Delta CFB .

In the following figure, M is mid-point of BC of a parallelogram ABCD. DM intersects the diagonal AC at P and AB produced at E. Prove that : PE = 2 PD .