Given Hilbert's axioms, show that the base angles of an isosceles triangle are congruent.Consider two triangles

ABC and

CBA. Notice that line AB
C*B* and notice that BC
B*A*, and angle ABC
C*B*A*. Using Hilbert's Axiom of Congruence (III-5), it implies that angles BAC
B*C*A*. We can further conclude that angle ABC
ACB, and the base angles of triangle ABC are congruent!