If bisectors of  ∠A  and  ∠B  of a quadrilateral  ABCD  intersect each other at  P , bisectors of  ∠B  and  ∠C  at  Q , bisectors of  ∠C  and  ∠D  at  R  and bisectors of  ∠D  and  ∠A  at  S , then PQRS is a

ABCD is a rhombus 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 rectangle.

ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA (see Fig 8.29). AC is a diagonal. Show that:(i) SR || AC and SR = 1/2 AC(ii) PQ = SR(iii) PQRS is a parallelogram.

ABCD is a trapezium in which AB||DC and AD = BC. If P, Q, R, S be respectively the mid points of BA, BD, CD and CA, then PQRS is a

ABCD is a parallelogram. P, Q, R and S are the points on sides AB, BC, CD and DA respectively such that AP = DR. If the area of the parallelogram ABCD is 16 cm2, find the area of the quadrilateral PQRS.

ABCD is a trapezium and P, Q are the mid points of the diagonals AC and BD respectively. Then PQ is equal to