Home
Class 9
MATHS
ABCD is a rhombus and P, Q, R and S are...

ABCD is a rhombus 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 rectangle.

Text Solution

Verified by Experts

Vertices as midpoint of quadrilateral from parallelogram
`/_ABD`
PS||BD
BD`_|_`AC
PS`_|_`AC
`/_ABC`
PQ||AC
AC`_|_`BD
...
Promotional Banner

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

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.

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

If ABCD be a rectangle and P, Q, R, S be the mid-points of AB, BC, CD and DA respectively, then the area of the quadrilateral PQRS is equal to

ABCD is a rectangle formed by the points A(1," "1)," "B(1," "4)," "C(5," "4)" "a n d" "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 yo

If DeltaABC is a equilateral triangle and P, Q, R are mid-points of sides AB, BC and CA respectively then-

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.

A ABCD is a rhombus and P,Q,R,S are the mid-points of AB,BC,CD,DA respectively.Prove that o+PQRS is a rectangle.

19.ABCD is a rectangle having length (x1) and breadth (x-1). If P,Q,R and S are the mid- points of sides AB,BC,CD and DA respectively,then the perimeter of quadrilateral PQRS is

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 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.