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For two triangles to be congruent, their corresponding sides must be of equal length. But for triangles to be similar, they must only have equal angles. For there to be a SAS postulate for similarity, the two corresponding sides would have to be proportionate, not equal. If they were equal, the triangles would be congruent.

So, an SAS postulate for similar triangles would mean that two of the sides of the smaller triangle are, for example, half the two corresponding sides of the other triangle. If also the corresponding included angles are equal, then the two triangles would be similar triangles.

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โˆ™ 2015-09-24 22:08:48
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โˆ™ 2014-06-24 22:41:41

No. SSA is ambiguous.

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Q: Is there an SAS postulate for similarity of two triangles also just as you have one for congruency of triangles?
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