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 ABC 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.

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.

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.

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.

In P Q R , S is any point on the side Q R . Show that P Q+Q R+R P >2P S

A B C D is a rhombus and P ,\ Q ,\ R ,\ S are the mid-points of A B ,\ B C ,\ C D ,\ D A respectively. Prove that P Q R S is a rectangle.

In the given triangle P, Q and R are the mid points of sides AB, BC and AC respectively. Prove that triangle PQR is similar to triangle ABC.

P,Q,R and S are the mid points of sides AB,BC , CD and DA respectively of rhombus ABCD. Show that PQRS is a rectangle. Under what conditions will PQRS be a square ?