Question

D, E and F are the mid points of side BC, CA and AB respectively of an equilateral triangle ABC. Show that DEF is also an equilateral triangle. ​

Answer 1

Answer:

Therefore DE=

2

1

AB,EF=

2

1

BC and FD=

2

1

AC

Now, ΔABC is an equilateral triangle

⇒AB=BC=CA

⇒

2

1

AB=

2

1

BC=

2

1

CA

⇒DE=EF=FD

∴ΔDEF is an equilateral triangle.