what if they don't give you the right angles? 

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The brightstorm video episode only applies to right triangles and it is really a special case of SAS. Because you know the hypotenuse are equal and one side is equal you can determine that the angle opposite the known legs are equal. They have to be complementary with the 3rd angle so the third angles are equal too. Those angles are the ones in between the leg and the hypotenuse so now you have a SAS proof. If the triangles are not right triangles, then you try SSS, ASA, SAS proofs.  You cannot use AAA for Congruence.