Question

Prove that the triangle formed by joining the mid points of an equilator triangle is also an equilator triangle

Answer 1

let tr ABC & midpts D of AB,E of AC,F of BC are given
when we join DE, it will be 1/2 of BC
similarly EF will be 1/2 of AB
DF will be 1/2 of AC
as ABC is equilateral
AB=BC=AC
1/2 of AB=1/2 of BC= 1/2 of AC
So, DEF is also equilateral