Question

d,e,f are are respectively the midpoint of the sides bc,ca,ab of an equilateral triangle.prove that d,e,f are also an equilateral triangle

Answer 1

Triangle ABC is an equilateral triangle.

⇒ AB = BC = AC

DE = 1/2 AB

EF = 1/2 BC

⇒ EF = 1/2 AB [Since AB = BC = AC]

DF = 1/2 AC

⇒ DF = 1/2 AB [Since AB = BC = AC]

DE = EF = DF

∴ ΔDEF is an equilateral triangle.