Question

An equilateral triangle is cut along its line of symmetry. How many isosceles triangles are formed?

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is A $0$

The figure is shown in image -

Let us assume $AB=AC=BC=d$

Now if we cut it along its line of symmetry i.e. perpendicular bisector of any one side (says $BC$) from point $A$ , 2 triangles are forms.

$\Delta ABD$ and $\Delta ACD$

Because $AD$ cuts the line $BC$ into 2 equal parts, hence $BD=CD=\frac{d}{2}$

And $A{B}^2=A{D}^2+B{D}^2$, ($AB=d$, $BD=\frac{d}{2}$)

hence $AD=\frac{\sqrt{3}d}{2}$

$AB\ne BD\ne AD$

Hence no Isosceles triangle will form.