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If the areas of two similar triangles are equal, prove that they are congruent.
D, E and F are respectively the mid-points of sides AB, BC and CA of Triangles ABC. Find the ratio of the areas of Triangles DEF and Triangles ABC.
Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.
Prove that the area of an equilateral triangle described on one side of a square is equal to half the area of the equilateral triangle described on one of its diagonals.
ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of triangles ABC and BDE is