Question

A quadrilateral ABCD is formed by joining the midpoints of the sides of a quadrilateral PQRS, taken in order. When ABCD will be a rectangle?​

Answer 1

Answer:

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..........................(1)

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

∴RS=

2

1

AC and RS∣∣AC

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

RS||PQ and RS=PQ

So PQRS is a parallelogram (Because pair of opposite side of a quadrilateral is equal and parallel)