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For triangles there are the standard similarity tests: AA, SAA, SAS, SSS and SSA (with angle opposite to the longer site).

I am looking for a good reference of those elementary theorems with complete proofs. Any suggestions?

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This website appears to offer proofs. The page I linked you to has five different proofs for SSS, and I think they must have proofs for everything else you mentioned.

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Thanks for nice link! However it would be better to have a book as a reference since I want to cite it. By the way the link is about congruence, my question was about similarity. –  Julia Sep 21 '12 at 15:02

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