Properties of Equality and Congruence

Vocabulary flashcards covering the properties of equality and properties of congruence.

Addition Property

If $a = b$ and $c = d$, then $a + c = b + d$.

Subtraction Property

If $a = b$ and $c = d$, then $a - c = b - d$.

Multiplication Property

If $a = b$, then $ca = cb$.

Division Property

If $a = b$ and $c \neq 0$, then $\frac{a}{c} = \frac{b}{c}$.

Substitution Property

If $a = b$, then either $a$ or $b$ may be substituted for the other in any equation (or inequality).

Reflexive Property

$$a = a$$

Symmetric Property

If $a = b$, then $b = a$.

Transitive Property

If $a = b$ and $b = c$, then $a = c$.

Reflexive Property of Congruence

$\overline{DE} \cong \overline{DE}$ and $\angle D \cong \angle D$

Symmetric Property of Congruence

If $\overline{DE} \cong \overline{FG}$, then $\overline{FG} \cong \overline{DE}$; if $\angle D \cong \angle E$, then $\angle E \cong \angle D$.

Transitive Property of Congruence

If $\overline{DE} \cong \overline{FG}$ and $\overline{FG} \cong \overline{JK}$, then $\overline{DE} \cong \overline{JK}$; if $\angle D \cong \angle E$ and $\angle E \cong \angle F$, then $\angle D \cong \angle F$.