`` ABCD 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.

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.

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.

A B C D is a rectangle formed by joining the points A(-1,\ -1),\ \ B(-1,\ 4),\ \ C(5,\ 4) and D(5,\ -1)dot P ,\ Q ,\ R and S are the mid-points of sides A B ,\ B C ,\ C D and D A respectively. Is the quadrilateral P Q R S a square? a rectangle? or a rhombus? Justify your answer.

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.

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 ?

ABCD is a rectangle formed by the points A(1,\ 1), B(1,\ 4), C(5,\ 4) and D(5,\ 1) . P, Q, R and S are the midpoints of AB, BC, CD and DA respectively. Is the quadrilateral PQRS a square? A rectangle? or a rhombus? Justify your answer.

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 Fig. 32, A B C D is a rectangle of length A B=40\ c m and breadth B C=25\ c mdot If P , Q , R , S be the mid-points of the sides A B ,\ B C ,\ C D\ and \ D A respectively, find the area of the shaded region.

In Figure, P Q > P R. Q S\ a n d\ R S are the bisectors of /_ Q and /_R respectively. Prove that S Q > S R .

In a A B C ,\ E\ a n d\ F are the mid-points of A C\ a n d\ A B respectively. The altitude A P to B C intersects F E\ at Q . Prove that A Q=Q P .