Modules · Module 02

Congruence and correspondence

Two triangles are congruent when one can be placed on the other by rigid motion. Correspondence of vertices is the whole game.

Sufficient conditions

SSS — three sides of one equal three sides of the other.

SAS — two sides and the included angle.

ASA — two angles and the included side.

AAS — two angles and a non-included side.

HL — hypotenuse and one leg, right triangles only.

SSA is not a congruence shortcut. It can produce zero, one, or two triangles (the ambiguous case).

AAA shows similarity, not congruence. The shapes match; the sizes may not.