when two triangle are similar, the ratio of the areas of those triangles is equal to the ratio of the square of their corresponding sides ( Area of similar triangle theorem).
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Theorem: If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides. This proves that the ratio of the area of two similar triangles is proportional to the squares of the corresponding sides of both the triangles.
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