Triangle Inequalities

The relationships between the sides and the angles of a triangle are expressed using inequalities.

Theorem. Side-Angle Inequality Theorem
If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side.

Restatement
In $\mathrm{\Delta ABC},$ if $\mathrm{BC}>\mathrm{AB}$ then $m\angle A>m\angle C.$