AC is a common diagonal to both the parallelograms ABCD and AECF. If the points B , E , D , F are not collinear , prove that BEDF is a parallelogram.

ABCD is quadrilateral E, F, G and H are the midpoints of AB, BC, CD and DA respectively. Prove that EFGH is a parallelogram.

If the point (a,b), (a',b') and (a-a',b-b') are collinear, then prove that ab' = a'b.

If the points (a,b), (a',b') and (a-a',b-b') are collinear, then prove that ab' = a'b.

P is any point on the diagonal BD of the parallelogram ABCD. Prove that DeltaAPD=DeltaCPD .

Prove that the points A (-2,-1) , B (5,4) C (6,7) and D (-1,2) are the vertices of a parallelogram.

The points E, F , G and H are on the sides AB, BC , CD and DA respectively of the rectangle ABCD , such that AE = BF = CG = DH . Prove that EFGH is a parallelogram.

In a triangle ABC, AD is the median drawn on the side BC is produced to E such that AD = ED prove that ABEC is a parallelogram.

If diagonals of a parallelogram bisect each other, prove that its a rhombus.

The area of the parallelogram ABCD is 44 sq.cm. P is the mid-point of BC. Determine the area of the DeltaABP .

The points B, C and R of the parallelograms ABCD and CPQR are collinear and BP || DR. If the area of the parallelogram ABCD be 44 sq.cm, then the area of DeltaPQR .