Question

ABCD is a rectangle. E,F,G and H are the mid point ofAB,BC,CD and DA respectively. EF ,FG,GH and HE are joined. Prove that EFGH is a rhombus.

Answer 1

GIVEN, quad ABCD
E,F,G,H are mid points
To Prove, EFGH is a parallelogram.


Proof,

Join AC and BD,
In ∆ADC

H is mid point of AD and G is mid point of DC.
So by mid point theorem,

HG || AC and HG= AC/2.......(1)

Similarly,

EF ||AC and EF =AC/2........(2)

By (1) & (2),

HG || EF and HG=AF

We know,
If in a quad opposite sides are equal and parallel then it is a parallelogram.

Hence proved

Answer 2

by mid point theorem it can prove