Question

In the following figure, $\angle AXY=\angle AYX.$ If
$\frac{BX}{AX}=\frac{CY}{AY},$ then the triangle ABC is isosceles.

• A. True
• B. False

Answer 1

The correct option is A True

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.