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Question

# The mid points of an equilateral triangle of side 10 cm are joined to form a triangle. What type of triangle is obtained by joining the mid points ?

A

Equilateral triangle of side 5√3cm

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B

Isosceles triangle in which the equal sides measure 5√2cm

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C

Isosceles triangle in which the unequal side measures 5√2cm

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D

Equilateral triangle of side 5cm

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Solution

## The correct option is D Equilateral triangle of side 5cm ABC is an equilateral triangle. D,E,F are mid points of sides AB , BC and AC respectively. By mid point theorem DE ||AC and DE = 12 AC ------------------I DF || BC and DF = 12 BC --------------- II EF || AB and EF = 12 AB ---------------III Since ABC is an equilateral triangle , AB = BC = AC Therefore, DE = DF = EF = 12 AB Hence, ΔDEF is equilateral with each side being 5cm.

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