Similar triangles are triangles having equal corresponding angle measures and proportional
corresponding side lengths. Equivalently, a similarity
maps one triangle onto the other. If 
is similar to 
, then
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The similarity criteria require less information than the definition. The AAA theorem, usually stated as the AA criterion, states that equality of two corresponding angles is sufficient, since the third pair is then also equal. The SAS similarity theorem requires equality of one pair of included angles and requires the two adjacent pairs of sides to be proportional. The SSS similarity theorem requires all three pairs of sides to be proportional. Equal corresponding angles do not by themselves fix the common scale, so similar triangles need not be congruent triangles.
