Home
Class 9
MATHS
P, Q, R and S are respectively the mid-p...

P, Q, R and S are respectively the mid-points of the sides AB, BC, CD and DA of a quadrilateral ABCD such that AC `bot` BD. Prove that 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

  • QUADRILATERALS

    NCERT ENGLISH|Exercise SOLVED EXAMPLES|8 Videos

  • PROBABILITY

    NCERT ENGLISH|Exercise SOLVED EXAMPLES|10 Videos

  • STATISTICS

    NCERT ENGLISH|Exercise Exercise 14.2|9 Videos

Similar Questions

Explore conceptually related problems

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 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.

If the sides of a quadrilateral ABCD touch a circle prove that AB+CD=BC+AD.

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 ?

P and Q are the mid-point of the opposite sides AB and CD of a parallelogram ABCD. AQ intersects DP at S and BQ intersects CP at R. Show that PQRS is a parallelogram.

In figure, P is the mid-point of side BC of a parallelogram ABCD such that angleBAP=angleDAP . Prove that AD = 2CD.

Show that in a quadrilateral ABCD AB+BC+CD+DA gt AC + BD

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

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.