Algebraic Reasoning and Properties of Equality

Vocabulary practice flashcards covering fundamental properties of equality, algebraic properties, and geometric formulas from Section 2.4: Algebraic Reasoning.

Addition Property of Equality

A property stating that adding the same number or quantity to both sides of an equation maintains equality: if $a = b$, then $a + c = b + c$.

Subtraction Property of Equality

A property stating that subtracting the same number or quantity from both sides of an equation maintains equality: if $a = b$, then $a - c = b - c$.

Multiplication Property of Equality

A property stating that multiplying both sides of an equation by the same quantity maintains equality: if $a = b$, then $ac = bc$.

Division Property of Equality

A property stating that dividing both sides of an equation by the same non-zero number maintains equality: if $a = b$ and $c \neq 0$, then $\frac{a}{c} = \frac{b}{c}$.

Reflexive Property of Equality

A property stating that any real number or geometric measure is equal to itself, expressed algebraically as $a = a$ (e.g., $x = x$ or $m\angle ABC = m\angle ABC$).

Symmetric Property of Equality

A property stating that if one quantity equals a second quantity, then the second quantity equals the first: if $a = b$, then $b = a$.

Transitive Property of Equality

A property stating that if a first quantity equals a second quantity and the second quantity equals a third, then the first quantity equals the third: if $a = b$ and $b = c$, then $a = c$.

Substitution Property of Equality

A property stating that if $a = b$, then $a$ may be replaced by $b$ (or vice versa) in any algebraic equation or geometric expression.

Distributive Property

An algebraic property stating that multiplying a sum by a number produces the same result as multiplying each addend individually by that number: $a(b + c) = ab + ac$.

Formula for the Area of a Trapezoid

The algebraic formula $A = \frac{1}{2}h(b_1 + b_2)$, where $A$ represents the area, $h$ is the height, and $b_1$ and $b_2$ are the lengths of the two parallel bases.

Formula for the Perimeter of a Rectangle

The algebraic formula $P = 2l + 2w$, where $P$ represents the perimeter, $l$ is the length, and $w$ is the width.