GeomP5 2.1­2.2 ­ Real Number Lines. Segments and Real Number Properties
Types of Numbers
Natural: Whole:
Integers:
Rational:
Irrational:
Real:
(Imaginary and Complex: Coming in Algebra 2!)
Number Line Postulate (2­1)
All real numbers can be found (in order) on a point on a number line, and every point on a number line represents a real number.
GeomP5 2.1­2.2 ­ Real Number Lines. Segments and Real Number Properties
Writing Rational and Real Numbers
Every rational number can be written as a fraction. In decimal form, it will either end or it will repeat.
Every irrational number can be written as a decimal, but it will never end, and never repeat.
Real Numbers on the Number Line
origin
coordinate
measure
absolute value
GeomP5 2.1­2.2 ­ Real Number Lines. Segments and Real Number Properties
Real Numbers on the Number Line
‐5‐4.3
‐2
1.6 3
Between Defined
In geometry, B is between A and C iff (if and only if):
(1) A, B, and C are collinear AND
(2) AB + BC = AC.
GeomP5 2.1­2.2 ­ Real Number Lines. Segments and Real Number Properties
Properties of Real Numbers (Found in segment measures)
Addition/Subtraction/Multiplication Property of Equality:
If a = b, then for any real number c:
• a + c = • a ­ c = • a * c = Also, if c ≠ 0: • a ÷ c = Properties of Real Numbers (Found in segment measures)
Reflexive Property of Equality:
Symmetric Property of Equality:
Transitive Property of Equality:
Substitution Property of Equality: