Question 440038
It is somewhat difficult to prove that angle congruence is an equivalence relation, because you have to go back to axioms and postulates that are already presumed, for example, two angles are congruent if and only if their measures are equal. Also, if angles A and B are congruent, then by the symmetric property, angles B and A are congruent. Also, if m(A) = m(B), and m(B) = m(C), then m(A) = m(C) by the transitive property. Obviously, m(A) = m(A), so angle congruence satisfies all three properties of equivalence relations.