Question

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

Answer 1

Length=l

Breadth=b

Let the diagonal intersect each other at $O$

As it can be seen from image

Side $EH=EF=FG=GH=\frac{\sqrt{l^2+b^2}}{2}$

Hence are all sides are $congruent$

Also, $EO=OG=\frac{b}{2}$

$HO=OF=\frac{l}{2}$

Hence the diagonal $bisect$ each other.

And as it can be seen from the figure that they intersect at ${90}^{\circ }$

Hence, due to all the reasons above it is a proved that the quadilateral formed is $rhombus$