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Prove that area of the equilateral triangle described on the side of a square is half of the area of

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Prove that area of the equilateral triangle described on the side of a square is half of the area of the equilateral triangle described on its diagonal.

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ΔBCE ~ ΔACE (equilateral Δ,s are equiangular) hence they similar by AAA similarity criterion ΔABC is a right triangle.

:. By Pythagoras theorem,

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