Hinge Theorem
Definition: If two sides of one triangle are congruent to two sides of another triangle and the included angles are not congruent, then the longer third side is across from the larger included angle.
Symbol/Notation: none
Statement: In the diagram shown above, we are given 2 triangles; Triangle ABC and Triangle DEF. We are also told that Segment AB is congruent to Segment DE and Segment BC is congruent to Segment EF. With this information, and by using the Hinge Theorem, we can conclude that Segment AC is longer than Segment DF, because Angle B is larger than Angle E.