Question

11 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​

Answer 1

Answer:

Given quadrilateral ABCD ,P,Q,R,S is the mid point of AB,BC,CD and AC

Join AC

In triangle ABC pis the mid point of AB and Q is the mid point of BC

∴PQ=

2

1

​

AC and PQ ∣∣AC.

Similarly in triangle ADC, R is the mid point of CD and S is the mid point of AD

∴RS=

2

1

​

AC and R S ∣∣ A C

From equation (1) and (2) , We get

RS||PQ and RS=PQ

So P Q R S is a parallelogram (Because pair of opposite side of a quadrilateral is equal and parallel)

Step-by-step explanation: