In Figure, `D ,E` and `F` are, respectively the mid-points of sides `B C ,C A` and `A B` of an equilateral triangle `A B C` . Prove that `D E F` is also an equilateral triangle.

Explanation

`"Proof: As ABC is an equilateral triangle

`therefore AB=BC=AC`-(1)

By midpoint theorem:

`EF=1/2 BC `

`DF=1/2 AC`

`DE=1/2 AB`

`therefore 1/2 AB=1/2 AC=1/2 BC`

`therefore EF=DF=ED`

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