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
• B. Isosceles triangle in which the equal sides measure 5√2cm
• C. Isosceles triangle in which the unequal side measures 5√2cm
• D. Equilateral triangle of side 5cm

Answer 1

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 = $\frac{1}{2}$ AC ------------------I

DF || BC and DF = $\frac{1}{2}$ BC --------------- II

EF || AB and EF = $\frac{1}{2}$ AB ---------------III

Since ABC is an equilateral triangle , AB = BC = AC

Therefore, DE = DF = EF = $\frac{1}{2}$ AB

Hence, ΔDEF is equilateral with each side being 5cm.