K, L, M and N are points on the sides AB, BC, CD and DA respectively of a square ABCD such that AK = BL = CM = DN. Prove that KLMN is a square.

ABCD is a square. P, Q, R, S are points on the sides AB. BC, CD, DA respectively such that AP = BQ = CR = DS. What is angleSPQ equal to ?

P, Q , R and S are respectively the mid-points of the sides AB, BC, CD and DA of a quadrilateral ABCD in which AC = BD. Prove that PQRS is a rhombus.

P, Q, R and S are respectively the mid-points of sides AB, BC, CD and DA of quadrilateral ABCD in which AC=BD and ACbotBD . Prove that PQRS is a square.

ABCD is a quadrilateral; P,Q,R and S are the points of trisection of side AB,BC,CD and DA respectively and are adjacent to A and C; prove that PQRS is parallelogram.

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.

Find the area of the shaded region in Fig. 3, where arcs drawn with centres A, B, C and D intersect in pairs at mid-points P, Q, R and S of the sides AB, BC, CD and DA respectively of a square ABCD of side 12 cm. [Use pi=3.14]

In the adjoining figure, ABCD is a quadrilateral. M and N are the points on AD and CD respectively such that AB = BC, angleABM=angleCBN and angleMBD=angleNBD . Prove that BM = BN .

Find the area of the shaded region in figure, in figure, where arcs drawn with centres A, B, C and D intersect in pairs at mid-point P, Q, R and S of the sides AB, BC, CD and DA, respectively of a square ABCD. (use pi = 3.14 )

Find the area of the shaded region in figure, where arcs drawn with centres A, B, C and D intersect in pairs at mid-point P, Q, R and S of the sides AB, BC, CD and DA, respectively of a square ABCD. (Use pi = 3.14 )