E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that `triangleABE ~ triangleCFB` .

P,Q are the mid points of the opposite side AB and CD of a parallelogram ABCD. AP intersects DP at S and BQ intersects CP at P. Show that PQRS is a parallelogram.

The sides AB and CD of a parallelogram ABCD are bisects at E and F. prove that EBFD is parallelogram.

E and F are points on diagonals AC of a parallelogram ABCD such that AE=CF. show that BFC parallelogram

A point is taken on the side BC of a parallelogram ABCD. AE and DC are produced to meet at F. Prove that : ar(ADF) = ar(ABFC)

Diagonal AC of a parallelogram ABCD bisects angleA show that ABCD is a rhombus.

ABCD s a trapezium in which AB||CD and AD=BC Show that: angleA=angleB

P is the mid point of the side CD of a paralellogram ABCD, a line thorugh C parallelogram to PA intersects AB at Q and DA produced by A. Prove that DA=AR and CQ=QR.

P and Q are points on opposite sides AD and BC of a parallelogram ABCD such that PQ passes through the point of intersection of its diagonals AC and BD. Show that PQ is bisected at O.

ABCD is a trapezium, in which AB||DC are a diagonal and E is the mid point of AD. A is drawn through E, parallel to AB intersect BC at F. Show that F is the mid point of BC