Question

In the following figure, $\angle AXY=\angle AYX$. If $\frac{BX}{AX}=\frac{CY}{AY}$, hence the $△$ ABC is an equilateral triangle
If the above statement is true then mention answer as 1, else mention 0 if false

Answer 1

In $△AXY$ and $△ABC$,
$\frac{BX}{AX}=\frac{CY}{AY}$
By converse of equal intercept theorem,
$BC\parallel XY$
Thus, $\angle ABC=\angle AXY$ and $\angle ACB=\angle AYX$ (Corresponding angles)
Also, $\angle AXY=\angle AYX$ (Given)
Thus, $\angle ABC=\angle ACB$
hence, $△ABC$ is an Isosceles triangle.