2.4 Properties of Equality and Congruence

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Notes

Algebra properties justify each step in solving and in proofs.

Addition/Subtraction: if $a = b$, then $a + c = b + c$. Multiplication/Division work the same way.
Substitution: if $a = b$, $b$ can replace $a$ in any expression.
Distributive: $a(b + c) = ab + ac$.
Reflexive: $a = a$. Symmetric: if $a = b$, then $b = a$. Transitive: if $a = b$ and $b = c$, then $a = c$.
The reflexive, symmetric and transitive properties also hold for congruence, like $\overline{AB} \cong \overline{AB}$.

Which property justifies: if $\angle A \cong \angle B$ and $\angle B \cong \angle C$, then $\angle A \cong \angle C$?

Solving $3(x - 2) = 12$, a student writes $3x - 6 = 12$. Which property justifies this step?

Which statement shows the Symmetric Property?