# The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle, if

a. PQRS is a rectangle

b. PQRS is a parallelogram

c. diagonals of PQRS are perpendicular

d. diagonals of PQRS are equal.

**Solution:**

Consider ABCD as a quadrilateral

P, Q, R and S are the midpoints of AB, BC, CD and AD

Let us now join AC

In triangle ABC,

P is the midpoint of AB

Q is the midpoint of BC

PQ = 1/2 BC and PQ is parallel to AC …. (i)

In triangle ADC,

R is the midpoint of CD

S is the midpoint of AD

RS = 1/2 AC and RS is parallel to AC …. (ii)

Using equation (i) and (ii)

RS || PQ and RS = PQ

So PQRS is a parallelogram

Therefore, the diagonals of PQRS are perpendicular.

**✦ Try This: **The quadrilateral formed by joining the mid-points of the sides of a quadrilateral ABCD, taken in order, is a rectangle, if

a. ABCD is a rectangle

b. ABCD is a parallelogram

c. diagonals of ABCD are perpendicular

d. diagonals of ABCD are equal.

**☛ Also Check:** NCERT Solutions for Class 9 Maths Chapter 8

**NCERT Exemplar Class 9 Maths Exercise 8.1 Problem 4**

## The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle, if, a. PQRS is a rectangle, b. PQRS is a parallelogram, c. diagonals of PQRS are perpendicular, d. diagonals of PQRS are equal

**Summary:**

The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle, if diagonals of PQRS are perpendicular

**☛ Related Questions:**

- The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in or . . . .
- If angles A, B, C and D of the quadrilateral ABCD, taken in order, are in the ratio 3:7:6:4, then AB . . . .
- If bisectors of ∠A and ∠B of a quadrilateral ABCD intersect each other at P, of ∠B and ∠C at Q, of ∠ . . . .

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