Question

D, E and F are the mid-points of the sides $AB,BC$ and $CA$ of an isosceles $\Delta ABC$ in which $AB=BC$. Then which of the following is correct:

• A. $△DEF$ is a scalene triangle
• B. $△DEF$ is an Isosceles triangle
• C. $△DEF$ is a right triangle
• D. $△DEF$ is a equilateral triangle

Answer 1

Answer: (B)

Given: $△ABC$, $AB=BC$, D, E and F are mid points of $AB$, $BC$ and $CA$ respectively.
Since, $D$ is mid point of $AB$ and $E$ is mid point of $BC$
By Mid point theorem, $DF\parallel AC$ and $DF=\frac{1}{2}AC$...(1)
Since, $E$ is mid point of $BC$ and $F$ is mid point of $AC$
By Mid point theorem, $EF\parallel AB$ and $EF=\frac{1}{2}AB$ ...(2)
Hence, By (1) and (2)
$DE=EF$
or $△DEF$ is an isosceles triangle.