Hinge theorem

In geometry, the hinge theorem states that if two sides of one triangle are congruent to two sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first triangle is longer than the third side of the second triangle.

The hinge theorem holds in Euclidean spaces and more generally in simply connected non-positively curved space forms.

The converse of the hinge theorem is also true: If the two sides of one triangle are congruent to two sides of another triangle, and the third side of the first triangle is greater than the third side of the second triangle, then the included angle of the first triangle is larger than the included angle of the second triangle.

In some textbooks, the theorem and its converse are written as the SAS Inequality Theorem and the SSS Inequality Theorem respectively.