Q:

# What is the correct theorem for proving that triangles are congruent?

A:

Four different methods for determining triangle congruency by examining sets of sides and angles exist: SSS (side, side, side), SAS (side, angle, side), ASA (angle, side, angle) and AAS (angle, angle, side). The hypotenuse and leg method can also determine the congruency of right triangles.

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Two triangles are congruent if they have three equal sets of sides and three equal sets of angles. SSS means that the three sides are equal on each triangle. SAS means that two sides and the included angle are equal on each triangle, while ASA means that two angles and the included side are equal. Finally, AAS means that two angles and the non-included side are equal on each triangle. Any of these triangles may be solved, that is, the given information and the knowledge that the triangles are congruent may be used to find the missing angles and sides.

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