Segment Measure and Coordinate Graphing

Real Numbers and Number Lines

NATURAL NUMBERS - set of counting numbers {1, 2, 3, 4, 5, 6, 7, 8…}

WHOLE NUMBERS – set of counting numbers plus zero {0, 1, 2, 3, 4, 5, 6, 7, 8…}

INTEGERS – set of the whole numbers plus their opposites {…, -3, -2, -1, 0, 1, 2, 3, …}

RATIONAL NUMBERS - numbers that can be expressed as a ratio of two integers a and b and includes fractions, repeating decimals, and terminating decimals

EXAMPLES OF RATIONAL NUMBERS = 3/ …= 2/3 0/5 = 0

IRRATIONAL NUMBERS - numbers that cannot be expressed as a ratio of two integers a and b and can still be designated on a number line

REAL NUMBERS Include both rational and irrational numbers

Coordinate  The number that corresponds to a point on a number line

Absolute Value  The number of units a number is from zero on the number line

Segments and Properties of Real Numbers

Betweeness  Refers to collinear points  Point B is between points A and C if A, B, and C are collinear and AB + BC = AC

Example  Three segment measures are given. Determine which point is between the other two.  AB = 12, BC = 47, and AC = 35

Measurement and Unit of Measure  Measurement is composed of the measure and the unit of measure  Measure tells you how many units  Unit of measure tells you what unit you are using

Precision  Depends on the smallest unit of measure being used

Greatest Possible Error  Half of the smallest unit used to make the measurement

Percent Error Greatest Possible Error x 100 measurement

Congruent Segments

 Two segments are congruent if and only if they have the same length

Theorems  Statements that can be justified by using logical reasoning

Theorem 2-1  Congruence of segments is reflexive

Theorem 2-2  Congruence of segments is symmetric

Theorem 2-3  Congruence of segments is transitive

Midpoint  A point M is the midpoint of a segment ST if and only if M is between S and T and SM = MT

Bisect  To separate something into two congruent parts

The Coordinate Plane

Coordinate Plane  Grid used to locate points  Divided by the y-axis and the x-axis into four quadrants  The intersection of the axes is the origin

 An ordered pair of numbers names the coordinate of a point  X-coordinate is first in the ordered pair  Y-coordinate is second in the ordered pair

Postulate 2-4  Each point in a coordinate plane corresponds to exactly one ordered pair of real numbers. Each ordered pair of real numbers corresponds to exactly one point in a coordinate plane.

Theorem 2-4  If a and b are real numbers, a vertical line contains all points (x, y) such that x = a, and a horizontal line contains all points (x, y) such that y = b.

Midpoints

Theorem 2-5 Midpoint formula for a line  On a number line, the coordinate of the midpoint of a segment whose endpoints have coordinate a and b is a+b. 2

Theorem 2-6 Midpoint formula for a Coordinate Plane  On a coordinate plane, the coordinates of the midpoint of a segment whose endpoints have coordinates (x 1, y 1 ) and (x 2, y 2 ) are (x 1 + x 2, y 1 + y 2 ) 2 2