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?
(3 marks)

Answer 1

$△$ABC is an equilateral triangle. D, E, and F are the 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)
(1 mark)

Since ABC is an equilateral triangle,

⇒ AB = BC = AC

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

Hence, ΔDEF is equilateral with each side being 5cm.
(1 mark)