The term congruent comes from the Latin word congruere, meaning "to come together." It therefore carries with it the idea of superposition, the idea that one of two congruent figures can be picked up and placed on top of the other with all parts coinciding. In the case of congruent triangles the parts would be the three sides and the three angles.
Two triangles are congruent if two sides and the included angle of one are congruent to two sides and the included angle of the other. This can be proven by super-imposing one triangle on the other. They have to match. Therefore the third side and the two other angles have to match. Modern authors typically make no attempt to prove it, taking it as a postulate instead.
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