# Inequalities

### Terms

Acute Angle  -  An angle with a measure of less than 90 degrees.
Addition Properties of Inequality  -  If a < b , then a + c < b + c
If a > b , then a + c > b + c
Greater Than  -  a > b if and only if there is a positive number c such that a - c = b .
Inequality  -  A statement that shows the relationship between two (or more) expressions with one of the following five signs: < , , > , , .
Inequality Properties of Opposites  -  If a > 0 , then - a < 0
If a < 0 , then - a > 0
Less Than  -  a < b if and only if there is a positive number c such that a + c = b .
Multiplication and Division Properties of Inequality  -  For positive numbers:
If a < b and c > 0 , then ac < bc and <
If a > b and c > 0 , then ac > bc and >
For negative numbers:
If a < b and c < 0 , then ac > bc and >
If a > b and c < 0 , then ac < bc and <
Obtuse Angle  -  An angle with a measure greater than 90 degrees, but not more than 180 degrees.
Property of Squares of Real Numbers  -  a 2≥ 0 for all real numbers a .
Right Angle  -  An angle with a measure of exactly 90 degrees.
Subtraction Properties of Inequality  -  If a < b , then a - c < b - c
If a > b , then a - c > b - c
Transitive Properties of Inequality  -  If a < b and b < c , then a < c .
If a > b and b > c , then a > c .
Trichotomy Property  -  For any two real numbers a and b , exactly one of the following is true: a < b , a = b , a > b .

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