# segment measure and coordinate graphing. real numbers and number lines

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Chapter 2

Chapter 2Segment Measure and Coordinate GraphingSection 2-1Real Numbers and Number LinesNATURAL 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= 2/30/5 = 0IRRATIONAL 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 NUMBERSInclude both rational and irrational numbersCoordinateThe number that corresponds to a point on a number lineAbsolute ValueThe number of units a number is from zero on the number lineSection 2-2Segments and Properties of Real NumbersBetweenessRefers to collinear pointsPoint B is between points A and C if A, B, and C are collinear and AB + BC = ACExampleThree segment measures are given. Determine which point is between the other two.AB = 12, BC = 47, and AC = 35Measurement and Unit of MeasureMeasurement is composed of the measure and the unit of measureMeasure tells you how many unitsUnit of measure tells you what unit you are usingPrecisionDepends on the smallest unit of measure being usedGreatest Possible ErrorHalf of the smallest unit used to make the measurementPercent ErrorGreatest Possible Error x 100 measurementSection 2-3Congruent SegmentsCongruent SegmentsTwo segments are congruent if and only if they have the same lengthTheoremsStatements that can be justified by using logical reasoningTheorem 2-1Congruence of segments is reflexiveTheorem 2-2Congruence of segments is symmetricTheorem 2-3Congruence of segments is transitiveMidpointA point M is the midpoint of a segment ST if and only if M is between S and T and SM = MTBisectTo separate something into two congruent partsSection 2-4The Coordinate PlaneCoordinate PlaneGrid used to locate pointsDivided by the y-axis and the x-axis into four quadrantsThe intersection of the axes is the origin

An ordered pair of numbers names the coordinate of a pointX-coordinate is first in the ordered pairY-coordinate is second in the ordered pairPostulate 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 2-4If 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 2-5MidpointsTheorem 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. 2Theorem 2-6Midpoint formula for a Coordinate PlaneOn 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