What is the hinge theorem?

The Hinge Theorem states that if two triangles have two pairs of corresponding sides that are in proportion, but the included angle of one triangle is larger than the included angle of the other, then the longer side (opposite the larger angle) of the first triangle is longer than the longer side of the second triangle (opposite the smaller angle). This theorem is used to compare the side lengths of triangles that have one side in common, or a "hinge." It is often used in geometry proofs to prove that certain triangles are similar.