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Answer congruence theoremSAS congruence theoremASA congruence theoremAAS congruence theoremHL congruence theorem

Explanation:

SSS stands for "Side side side" indicating there are 3 pairs of sides that are same length. Visually we use tickmarks to show how the sides pair up. Eg: sides that have 1 tickmark only are the same length. If we know that all 3 pairs of sides are congruent, then we have enough info to conclude the triangles are congruent.SAS means "side angle side". The angle is between the two sides. The sides in question are the ones with tickmarks to indicate how they pair up. We have two angles and a side between them. So we use ASA this time. It stands for "Angle side angle". This is slightly different from AAS.We'll use AAS here. The side is not between the two angles. So this is why AAS is different from ASA. Some books may call "AAS" as "SAA", but they're the same thing. HL stands for hypotenuse leg. This only applies to right triangles (since the hypotenuse is a special term for the longest side of a right triangle). The hypotenuse is always opposite the 90 degree angle. This is the only time when SSA will work. Otherwise, SSA is ambiguous and it is not a valid congruence theorem.