How to Prove two triangles are Similar ,they are congruent?


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If two triangles are similar all their dimensions are in the same ratio. The area of a triangle is half the base times the height. If the ratio of the corresponding sides is R, and the height and base of one triangle are h and b, then the height and base of the other will be Rh and Rb and its area is (1/2)R^2hb, while the other triangle's area is (1/2)hb. If these areas are equal, R^2hb=hb, so R=1 or -1, which means that the sides of one triangle are equal in length to the corresponding sides in the other, and, by definition of similarity, the corresponding angles are equal. Therefore, the triangles are congruent. The triangles can be reflections of one another.

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