Properties of Equality and Congruency

Addition Property of Equality

If equal quantities are added to each side of an equation, the equality is maintained.

Subtraction Property of Equality

If equal quantities are subtracted from each side of an equation, the equality is maintained.

Multiplication Property of Equality

If equal quantities are multiplied on each side of an equation, the equality is maintained.

Division Property of Equality

If equal quantities are divided from each side of an equation, the equality is maintained.

Reflexive Property of Equality

A quantity is equal to itself, stated as a = a. (known as a ‘duh’ statement in mathematics)

Reflexive Property of Congruence

A geometric figure is congruent to itself, expressed as ( \triangle ABC \cong \triangle ABC ). (also known as a ‘duh’ statement in math)

Symmetric Property of Equality

If one quantity equals a second, then the second equals the first, expressed as if a = b, then b = a.

Symmetric Property of Congruence

If one geometric figure is congruent to a second, then the second is congruent to the first, expressed as if \triangle ABC \cong \triangle DEF, then \triangle DEF \cong \triangle ABC.

Transitive Property of Equality

If one quantity equals a second and the second equals a third, then the first equals the third, expressed as if a = b and b = c, then a = c. (known as a middleman property)

Transitive Property of Congruence

If one geometric figure is congruent to a second and the second is congruent to a third, then the first is congruent to the third, expressed as if \triangle ABC \cong \triangle DEF and \triangle DEF \cong \triangle GHI, then \triangle ABC \cong \triangle GHI. (also known as a middleman property)

Substitution Property of Equality

If a equals b, then b can be substituted for a in any expression or equation, maintaining equality. For example, if a = b, then a + c = b + c.

Substitution Property of Congruence

If two geometric figures are congruent, one can be substituted for the other in expressions and equations without changing the equality. This property ensures that relationships involving congruent figures remain valid.