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Suppose two triangles are similar and one pair of sides of the triangles are congruent. Are the triangles necessarily congruent? Explain your reasoning.​

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Answer:

Yes. For the triangles to be similar, all of the sides have to be proportionate to its corresponding side. If the ratio of one of the pairs sides of the triangles is 1:1, then all of the pairs of sides on the triangles have to also have a ratio of 1:1. Using this, according to SSS postulate, the two triangles are similar. With the given information, either both triangles are congruent, or they are not similar.

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