OME SOLVED PROBLEMS ON MIDPOINT THEOREMXAMPLE 1 If D, E and F are resp

1.	OME SOLVED PROBLEMS ON MIDPOINT THEOREMXAMPLE 1 If D, E and F are respectively themidpoints of the sides BC, CA and ABof an equilateral triangle ABC, provethat ADEF is also an equilateraltriangle.
Answer» Triangle ABC is an equilateral triangle.⇒ AB = BC = ACDE = 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.

OME SOLVED PROBLEMS ON MIDPOINT THEOREMXAMPLE 1 If D, E and F are respectively themidpoints of the sides BC, CA and ABof an equilateral triangle ABC, provethat ADEF is also an equilateraltriangle.

Answer»

Triangle ABC is an equilateral triangle.⇒ AB = BC = ACDE = 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.