Consider the isosceles triangles [math]\triangle ABC[/math] and [math]\triangle CBA[/math]. Notice that [math]\overline{AB}\cong\overline{CB},\overline{BC}\cong\overline{BA},[/math] and [math]\angle ABC\cong\angle CBA.[/math] Thus, by the application of Hilbert's Axiom of Congruence III-5, we know that [math]\triangle ABC\cong\triangle CBA[/math]. We can further conclude that [math]\angle BAC\cong\angle BCA.[/math] Thus, in triangle [math]\triangle ABC[/math] the base angles, [math]\angle BAC[/math] and [math]\angle BCA[/math] are congruent.