In the diagram below, P and Q are midpoints of sides BC and AD respectively of the parallelogram ABCD. If side AB = diagonal BD: prove that the quadrilateral BPDQ is a rectangle.

If P and Q are the middle points of the sides BC and CD of the parallelogram ABCD, then AP+AQ is equal to

L and M are the mid-points of sides AB and DC respectively of parallelogram ABCD. Prove that segments DL and BM trisect diagonal AC.

P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD . Show that a r\ (A P B)\ =\ a r\ (B Q C) .

D, E and F are the mid-points of the sides BC, CA and AB respectively of triangle ABC. Prove that: BDEF is a parallelogram.

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.

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 the figure above, P and Q are the midpoints of sides AB and BC, respectively, of square ABCD. Line segment PB is extended by its own length to point E, and line segment PQ is extended to point F so that FEbotPE . If the area of square ABCD is 9, what is the area of quadrilateral QBEF?

ABCD is a rhombus and P, Q, R and S are wthe mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.

ABCD is a parallelogram. P and Q are the mid-points of sides AB and AD reapectively. Prove that area of triangle APQ= (1)/(8) of the area of parallelogram ABCD.

ABCD is a parallelogram. P and Q are the mid-points of sides AB and AD reapectively. Prove that area of triangle APQ= (1)/(8) of the area of parallelogram ABCD.