In the following figure, ∠AXY = ∠AYX. If BX/AX = CY/AY, show that triangle ABC is isosceles.

Given, ∠AXY = ∠AYX So, AX = AY = a (let) [Sides opposite to equal angles are equal.] Given, From figure, AB = AX + XB = a + b. AC = AY + CY = a + b. So, AB = AC. Hence, proved that ∆ABC is an isosceles triangle.

Mathematics

In the following figure, ∠AXY = ∠AYX.
If $\dfrac{BX}{AX} = \dfrac{CY}{AY}$ , show that triangle ABC is isosceles.

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Given,

∠AXY = ∠AYX

So, AX = AY = a (let) [Sides opposite to equal angles are equal.]

Given,

$\Rightarrow \dfrac{BX}{AX} = \dfrac{CY}{AY} \\[1em] \Rightarrow \dfrac{BX}{a} = \dfrac{CY}{a} \\[1em] \Rightarrow BX = CY = b.$

From figure,

AB = AX + XB = a + b.

AC = AY + CY = a + b.

So, AB = AC.

Hence, proved that ∆ABC is an isosceles triangle.

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Mathematics

In the following figure, ∠AXY = ∠AYX.
If $\dfrac{BX}{AX} = \dfrac{CY}{AY}$ , show that triangle ABC is isosceles.

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