CHAPTER 2
Segment Measure and Coordinate Graphing
SECTION 2-1
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
0.375 = 3/80.66666…= 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
SECTION 2-2
Segments and Properties of Real Numbers
Betweeness
Refers to collinear pointsPoint 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
PrecisionDepends 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
SECTION 2-3Congruent Segments
Congruent Segments
Two segments are congruent if and only if they have the same length
TheoremsStatements that can be justified by using logical reasoning
Theorem 2-1Congruence 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
BisectTo separate something into two congruent parts
SECTION 2-4The Coordinate Plane
Coordinate PlaneGrid 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 2-4Each 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.
SECTION 2-5Midpoints
Theorem 2-5Midpoint formula for a
lineOn a number line, the coordinate of the midpoint of a segment whose endpoints have coordinate a and b is a+b.
2
Theorem 2-6Midpoint formula for a
Coordinate Plane On a coordinate plane, the coordinates of the midpoint of a segment whose endpoints have coordinates (x1, y1) and (x2, y2) are
(x1 + x2 , y1 + y2)
2 2
