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SAS Similarity Theorem

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SASSimilarityTheorem

The SAS similarity theorem states that two triangles are similar triangles if one pair of corresponding angles is equal and the lengths of the two pairs of corresponding sides that include those angles are proportional. Thus, if ∠A=∠A^' and

(AB)/(A^'B^')=(AC)/(A^'C^'),

then DeltaABC and DeltaA^'B^'C^' are similar triangles. Unlike the SAS theorem for congruent triangles, the SAS similarity theorem requires corresponding side lengths to be proportional rather than equal.

See also

SAS Theorem, Similar Triangles, SSS Similarity Theorem, Triangle Similarity Theorems

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References

Coxeter, H. S. M. and Greitzer, S. L. Geometry Revisited. Washington, DC: Math. Assoc. Amer., 1967.

Cite this as:

Weisstein, Eric W. "SAS Similarity Theorem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SASSimilarityTheorem.html

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