Mathematics

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

True

##### SOLUTION
In $\triangle AXY$ and $\triangle ABC$,
$\dfrac{BX}{AX} = \dfrac{CY}{AY}$

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, $\triangle ABC$ is an Isosceles triangle.

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TRUE/FALSE Medium Published on 09th 09, 2020
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