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Question : ABC is an equilateral triangle points D, E and F are taken in sides AB, BC and CA respectively so that, AD = BE = CF. Then DE, EF, and FD enclose a triangle which is:

Option 1: equilateral

Option 2: isosceles

Option 3: right angled

Option 4: none


Team Careers360 21st Jan, 2024
Answer (1)
Team Careers360 23rd Jan, 2024

Correct Answer: equilateral


Solution :
Given: ABC is an equilateral triangle points D, E and F are taken in sides AB, BC and CA respectively so that, AD = BE = CF.
Now, AB = BC = CA and AD = BE = CF
So, AD = BD = BE = EC = CF = AF
⇒D, E, and F are midpoints of the sides AB, BC and AC, respectively.
Thus, DF || BC and DF = $\frac{1}{2}$BC
Similarly DE = $\frac{1}{2}$AC and EF = $\frac{1}{2}$AB
So, DE = EF = DF
$\therefore \triangle$DEF is an equilateral triangle.
Hence, the correct answer is equilateral.

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