Question 440038: Please help me solve this proof- Use the definition of angle congruence to prove that angle congruence is an equivalence relation. That is, prove that angle congruence is reflexive, symmetric, and transitive.
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! 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.
|
|
|
