How are congruent triangles defined?

Congruent triangles are defined as triangles in which all corresponding sides and angles are equal. This means that if one triangle can be perfectly mapped onto another using rigid transformations like rotation, reflection, or translation, then the triangles are congruent.

For two triangles to be congruent, each side of one triangle must match exactly in length with the corresponding side of the other triangle, and the angles must also be equal in measure. This relationship ensures that the triangles are identical in shape and size, even if their positions are different in space.

Understanding congruence is fundamental in geometry, as it allows for the establishment of equality between different geometric figures, enabling the solving of various problems related to triangles.