In the adjacent figure ABCD is a parallelogram P and Q are the midpoints of sides AB and DC respectively. Show that PBCQ is also 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.

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

In the adjacent figure ABCD is a parallelogram and E is the midpoint of the side BC. If DE and AB are produced to meet at F, show that AF = 2AB .

In the adjacent figure, we have AC = XD, C and D are mid points of AB and XY respectively. Show that AB = XY.

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

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 the adjacent figure ABCD is a parallelogram ABEF is a rectangle show that DeltaAFD~=DeltaBEC .

In a parallelogram ABCD, E and F are the mid points of sides AB and CD respectively (see fig.) Show that the line segements AF and EC trisect the diagonal BD.

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

ABCD is a quadrilateral in which P, Q, R and S are mid- points of the sides AB, BC, CD and DA. AC is a diagonal. Show that : PQRS is a parallelogram.