SAS and SSS Similarity Theorems

Students learn the following theorems related to similar triangles. If an angle of one triangle is congruent to an angle of another triangle, and the lengths of the sides that include each angle are in proportion, then the triangles are similar (Side-Angle-Side Similarity Theorem, or SAS Similarity Theorem). If the lengths of the sides of two triangles are in proportion, then the triangles are similar (Side-Side-Side Similarity Theorem, or SSS Similarity Theorem). Students are then asked to determine whether given triangles are similar based on these theorems.

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