Congruence (geometry).

Congruence (geometry). Congruence (geometry), the relationship between two- or three-dimensional figures having the exact same size and shape. All of the corresponding sides of two congruent figures are the same length, and all of the corresponding angles are equal. Directly congruent figures can be slid so that they are superimposed, coinciding everywhere. Inversely congruent figures are mirror images of each other that must be flipped over to be superimposed. Congruence is most often encountered when studying triangles. There are three rules that determine whether two triangles are congruent. If any one of these rules holds, then the triangles are congruent: (1) The lengths of all three sides of the first triangle are equal to the lengths of the sides of the second. (It is not sufficient for the angles of one triangle to be equal to the angles of the other; the triangles could still differ in size.) (2) Two sides of the first triangle and the included angle (the angle between those two sides) are equal to two sides and their included angle in the second triangle. (3) Two angles and one of the sides in the first triangle are equal to the corresponding angles and side in the second triangle. Microsoft ® Encarta ® 2009. © 1993-2008 Microsoft Corporation. All rights reserved.