Question

ABCD is quadrilateral E,F,G and H are the midpoints of AB,BC,CDandDA respectively .prove that EFGH is a rhombus

Answer 1

ar(quadrilateral ABCD ) = ar ( Rhombus EFGH )

Answer 2

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