Congruent Triangles

Definition: Two figures are said to be Congruent if they have exactly the same shape and size.

Introduction: When naming congruent triangles, it is important to give the letters in the correct order so that it is clear which sides of the triangles correspond to each other. When congruent triangles are properly named, it is possible to find pairs of equal sides or equal angles without looking at the figure.

Note that in geometry the symbol \( \scriptsize \equiv \) means identically equal to”, or “is Congruent to”.

Therefore, ∆ABC \( \scriptsize \equiv \) ∆XYZ is short for “triangle ABC is congruent to triangle XYZ. The following gives the four sets of conditions for the congruency of two triangles.

Two triangles are congruent if: