Properties of Equality and Congruence

Question 1

Addition-Subtraction Property of Equality

Answer 1

The same number can be added to/subtracted from both sides of an equation.

If a = b, then a + c = b + c. a - c = b - c.

Question 2

Multiplication Property of Equality

Answer 2

The same number can be mulitplied to both sides of an equation.

If a = b, then a * c = b * c.

Question 3

Division Property of Equality

Answer 3

Both sides of an equation can be divided by the same non-zero number.

If a = b, then a/c = b/c (c ≠ 0).

Question 4

Reflexive Property of Equality-Congruence

Answer 4

A number is equal to itself.

a = a

Line AB is congruent to line AB.

Question 5

Symmetric Property of Equality/Congruence

Answer 5

The order of an equality can be reversed.

If a = b, then b = a.

If If line AB is congruent to line CD, then line CD is congruent to line AB.

Question 6

Transitive Property of Equality/Congruence

Answer 6

If two numbers are equal to the same number, those numbers are equal.

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

If line AB is congruent to line CD and line CD is congruent to line EF, then line AB is congruent to line EF.

Question 7

Substitution Property of Equality

Answer 7

If two numbers are equal, you can replace one with the other in an expression.

If a = b, then b can be substituted for a in any expression.

Question 8

Distributive Property

Answer 8

Multiply the number outside the parentheses with each term inside the parentheses.

a(b + c) = ab + ac