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प्रश्न
In the following figure, ∠AXY = ∠AYX. If `(BX)/(AX) = (CY)/(AY)`, show that triangle ABC is isosceles.
उत्तर
In the given figure,
∠AXY = ∠AYX
And `(BX)/(AX) = (CY)/(AY)`
To prove: ΔABC is an isosceles triangle
In ΔAXY
∠AXY = ∠AYX ...(Given)
∴ AY = AX ...(Sides opposite to equal angles)
`(BX)/(AX) = (CY)/(AY) => (AX)/(BX) = (AY)/(CY)`
∴ XY || BC
∴ ∠B = ∠AXY and ∠C = ∠AYX ...(Corresponding angles)
But ∠AXY = ∠AYX is given
∴ ∠B = ∠C
∴ AC = AB ...(Side opposite to equal angles)
∴ ΔABC is an isosceles triangle.
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