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 :(i) `S R\ ||\ A C`and `S R=1/2A C`(ii) `P Q\ =\ S R`(iii) PQRS is a parallelogram

Prove that the figure formed by joining the mid-points of the pair of consecutive sides of a quadrilateral is a parallelogram. OR B A C D is a parallelogram in which P ,Q ,R and S are mid-points of the sides A B ,B C ,C D and D A respectively. A C is a diagonal. Show that : P Q|| A C and P Q=1/2A C S R || A C and S R=1/2A C P Q=S R (iv) P Q R S is a parallelogram.

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.

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 quadirlateral in which AD= BC. If P,Q,R,S be the midpoints of AB,AC,CD and BD respectively, show that PQRS is a rhombus.

Suppose ABCD is a rectangled and P,Q,R,S are points on the sides AB,BC,CD,DA respectively. Show that PQ+QR+RS+SP gt sqrt(2) AC .

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 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.

Let ABCD be a rectangle. Let P, Q, R, S be the mid-points of sides AB, BC, CD, DA respectively. Then the quadrilateral PQRS is a

ABCD is a parallelogram in which P and Q are mid-points of opposite sides AB and CD (see Fig. 8.18). If AQ intersects DP at S and BQ intersects CP at R, show that: (i) APCQ is a parallelogram. (ii) DPBQ is a parallelogram. (iii) PSQR is a parallelogram