congruents

In geometry, two figures are considered congruent if they have the same shape and the same size. This means that one figure can be transformed into the other through a sequence of rigid motions, which include translations, rotations, and reflections. Congruent figures are essentially identical copies of each other, differing only in their position or orientation in space.

For line segments, congruence means they have the same length. Two angles are congruent if they have the same measure. For triangles, congruence is established if all three corresponding sides are equal in length and all three corresponding angles are equal in measure. There are specific congruence postulates and theorems, such as SSS (Side-Side-Side), SAS (Side-Angle-Side), ASA (Angle-Side-Angle), and AAS (Angle-Angle-Side), that allow us to determine if two triangles are congruent without verifying all six corresponding parts.

The concept of congruence is fundamental in geometry and is used in proofs, constructions, and in understanding symmetry. When objects are congruent, they possess all the same geometric properties. For example, if two triangles are congruent, their perimeters, areas, and other measurable attributes will also be identical. The symbol used to denote congruence is typically an equals sign with a tilde above it.