Properties of Equality Quiz

Properties of Equality

• Addition Property of Equality: If ( a = b ), then ( a + c = b + c ); allows adding the same value to both sides of an equation.
• Subtraction Property of Equality: If ( a = b ), then ( a - c = b - c ); allows subtracting the same value from both sides of an equation.
• Multiplication Property of Equality: If ( a = b ), then ( ac = bc ); allows multiplying both sides of an equation by the same value.
• Division Property of Equality: If ( a = b ) and ( c \neq 0 ), then ( \frac{a}{c} = \frac{b}{c} ); allows dividing both sides of an equation by the same non-zero value.
• Substitution Property of Equality: If ( a = b ), then ( a ) can replace ( b ) in any equation or expression; essential for simplifying expressions or solving equations.

Distributive Property

• Distributive Property: ( a(b + c) = ab + ac ); describes how to distribute multiplication over addition.

Reflexive Property of Equality

• Reflexive Property (Real Numbers): For any real number ( a ), ( a = a ); establishes that any quantity is equal to itself.
• Reflexive Property (Segment Length): For any segment ( AB ), ( AB = AB ); applies to geometric segments, signifying congruence.
• Reflexive Property (Angle Measure): For any angle, its measure is equal to itself; crucial in the context of geometric angles.