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# Properties of Equality and Congruence

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Properties of Equality and Congruence

### Vocabulary Language: English Spanish

properties of equality

properties of equality

Together with properties of congruence, the logical rules that allow equations to be manipulated and solved.

You can add a quantity to both sides of an inequality and it does not change the sense of the inequality. If $x > 3$, then $x+2 > 3+2$.
distributive property

distributive property

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, $a(b + c) = ab + ac$.
Division Property of Inequality

Division Property of Inequality

The division property of inequality states that two unequal values divided by a positive number retain the same relationship. Two unequal values divided by a negative number result in a reversal of the relationship.
Multiplication Property of Equality

Multiplication Property of Equality

The multiplication property of equality states that if the same constant is multiplied to both sides of the equation, the equality holds true.
Real Number

Real Number

A real number is a number that can be plotted on a number line. Real numbers include all rational and irrational numbers.
Reflexive Property of Congruence

Reflexive Property of Congruence

$\overline{AB} \cong \overline{AB}$ or $\angle B \cong \angle B$
Reflexive Property of Equality

Reflexive Property of Equality

Any algebraic or geometric item is equal in value to itself.
Right Angle Theorem

Right Angle Theorem

The Right Angle Theorem states that if two angles are right angles, then the angles are congruent.
Same Angle Supplements Theorem

Same Angle Supplements Theorem

The Same Angle Supplements Theorem states that if two angles are supplementary to the same angle then the two angles are congruent.
Substitution Property of Equality

Substitution Property of Equality

If a variable is equal to a specified amount, that amount can be directly substituted into an equation for the given variable.
Subtraction Property of Equality

Subtraction Property of Equality

The subtraction property of equality states that you can subtract the same quantity from both sides of an equation and it will still balance.
Symmetric Property of Congruence

Symmetric Property of Congruence

If $\overline{AB} \cong \overline{CD}$, then $\overline{CD} \cong \overline{AB}$. Or, if $\angle ABC \cong \angle DEF$, then $\angle DEF \cong \angle ABC$
Transitive Property of Congruence

Transitive Property of Congruence

If $\overline{AB} \cong \overline{CD}$ and $\overline{CD} \cong \overline{EF}$, then $\overline{AB} \cong \overline{EF}$. Or, if $\angle ABC \cong \angle DEF$ and $\angle DEF \cong \angle GHI$, then $\angle ABC \cong \angle GHI$
Transitive Property of Equality

Transitive Property of Equality

If a = 5, and b = 5, then a = b.
Vertical Angles Theorem

Vertical Angles Theorem

The Vertical Angles Theorem states that if two angles are vertical, then they are congruent.