## What are the 5 properties of equality?

The Reflexive Property. a =a.

• The Symmetric Property. If a=b, then b=a.
• The Transitive Property. If a=b and b=c, then a=c.
• The Substitution Property. If a=b, then a can be substituted for b in any equation.
• The Addition and Subtraction Properties.
• The Multiplication Properties.
• The Division Properties.
• The Square Roots Property*
• What is an example of subtraction property of equality?

Subtraction property of equality refers to balancing an equation by using the same mathematical operation on both sides. If we take away 2 stars from Circle 1 then, to balance this equation in both the circles we need to take away 2 stars from the other circle also.

Is there a distributive property of equality?

The distributive property states that the product of an expression and a sum is equal to the sum of the products of the expression and each term in the sum. For example, a(b + c) = ab + ac. The division property of inequality states that two unequal values divided by a positive number retain the same relationship.

### How do you prove equality?

Proving Set Equality. One way to prove that two sets are equal is to use Theorem 5.2 and prove each of the two sets is a subset of the other set. In particular, let A and B be subsets of some universal set. Theorem 5.2 states that A=B if and only if A⊆B and B⊆A.

What is the symmetric property of equality?

In mathematics, the symmetric property of equality is really quite simple. This property states that if a = b, then b = a. That is, we can interchange the sides of an equation, and the equation is still a true statement.

What are the different properties of equality?

PROPERTIES OF EQUALITY
Reflexive Property For all real numbers x , x=x . A number equals itself.
Addition Property For all real numbers x,y, and z , if x=y , then x+z=y+z .
Subtraction Property For all real numbers x,y, and z , if x=y , then x−z=y−z .

#### Is a subtraction property of equality?

The subtraction property of equality tells us that if we subtract from one side of an equation, we also must subtract from the other side of the equation to keep the equation the same. To keep them the same, you have to do the same to both sides of the equation.

What is the multiplicative property of equality?

Multiplication Property of Equality Stated simply, when you divide or multiply both sides of an equation by the same quantity, you still have equality. In the example below the variable is multiplied by 4 , so we will divide both sides by 4 to “undo” the multiplication.

What are the properties of equality and congruence?

There are three very useful theorems that connect equality and congruence. Two angles are congruent if and only if they have equal measures. Two segments are congruent if and only if they have equal measures. Two triangles are congruent if and only if all corresponding angles and sides are congruent.