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 $\sqrt{3}$cm
• B. Isosceles triangle, in which the equal sides measure 5 $\sqrt{2}$cm
• C. Isosceles triangle, in which the unequal side measures 5 $\sqrt{2}$cm
• 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 and F are mid points of sides AB, AC and BC respectively.

By mid point theorem,

DE ||BC and DE = $\frac{1}{2}$ BC --------------- I

DF || AC and DF = $\frac{1}{2}$ AC -------------- 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 $\frac{10}{2}=$ 5 cm.