Question

Prove that the quadrilateral formed by joining the mid-points of rectangle is rhombus.

Answer 1

Step-by-step explanation:

ABCD be the rectangle and P, Q, R and S be the midpoints of AB, BC, CD and DA, respectively.

Join diagonals of the rectangle.

In ∆ ABC, we have, by midpoint theorem,

∴ PQ ∣∣ AC and PQ =

AC

Similarly, SR ∣∣ AC and SR =

AC.

As, PQ ∣∣ AC and SR ∣∣ AC, then also PQ ∣∣ SR

Also, PQ = SR, each equal to

AC …(1)

So, PQRS is a parallelogram