Homework 12 Segments And Rays Answers To Logo
Presentation on theme: "Lesson 12: Segments and Rays"— Presentation transcript:
1 Lesson 12: Segments and Rays
2 Lesson 12: Segments and Rays
PostulatesDefinition: An assumption that needs no explanation.Examples:Through any two points there isexactly one line.A line contains at least two points.Through any three points, there isexactly one plane.A plane contains at least three points.Lesson 12: Segments and Rays
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PostulatesExamples:If two planes intersect,then the intersecting is a line.If two points lie in a plane,then the line containing the twopoints lie in the same plane.Lesson 12: Segments and Rays
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The Ruler PostulateThe Ruler Postulate: Points on a line can be paired with the real numbers in such a way that:Any two chosen points can be paired with 0 and 1.The distance between any two points on a number line is the absolute value of the difference of the real numbers corresponding to the points.Formula: Take the absolute value of the difference of the two coordinates a and b: │a – b │Lesson 12: Segments and Rays
5 Ruler Postulate : Example
Find the distance between P and K.Note: The coordinates are the numbers on the ruler or number line!The capital letters are the names of the points.Therefore, the coordinates of points P and K are 3 and 2 respectively.Substituting the coordinates in the formula │a – b │PK =  = 5Remember : Distance is always positiveLesson 12: Segments and Rays
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BetweenDefinition: X is between A and B if AX + XB = AB.AX + XB = ABAX + XB > ABLesson 12: Segments and Rays
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Definition:Part of a line that consists of two points called the endpoints and all points between them.How to sketch:How to name:AB (without a symbol) means the length of the segment or the distance between points A and B.Lesson 12: Segments and Rays
8 The Segment Addition Postulate
If C is between A and B, then AC + CB = AB.Example:If AC = x , CB = 2x and AB = 12, then, find x, AC and CB.2xx12Step 1: Draw a figureStep 2: Label fig. with given info.AC + CB = ABx x = 123x = 12x = 4Step 3: Write an equationx = 4AC = 4CB = 8Step 4: Solve and find all the answersLesson 12: Segments and Rays
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Congruent SegmentsDefinition:Segments with equal lengths. (congruent symbol: )Congruent segments can be marked with dashes.If numbers are equal the objects are congruent.AB: the segment AB ( an object )AB: the distance from A to B ( a number )Correct notation:Incorrect notation:Lesson 12: Segments and Rays
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MidpointDefinition:A point that divides a segment intotwo congruent segmentsFormulas:On a number line, the coordinate of the midpoint of a segment whose endpoints have coordinates a and b isIn a coordinate plane, the coordinates of the midpoint of a segment whose endpoints have coordinates andisLesson 12: Segments and Rays
11 Midpoint on Number Line  Example
Find the coordinate of the midpoint of the segment PK.Now find the midpoint on the number line.Lesson 12: Segments and Rays
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Segment BisectorDefinition:Any segment, line or plane that divides a segment into two congruent parts is called segment bisector.Lesson 12: Segments and Rays
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Definition:RA : RA and all points Y such thatA is between R and Y.How to sketch:How to name:( the symbol RA is read as “ray RA” )Lesson 12: Segments and Rays
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Opposite RaysDefinition:If A is between X and Y, AX and AY are opposite rays.( Opposite rays must have the same “endpoint” )opposite raysnot opposite raysLesson 12: Segments and Rays
Objective:
The student will be able to define segment, ray, opposite rays, congruent, midpoint, bisect, length and postulate. The "Ruler Postulate" and "Segment Addition Postulate" will be introduced.
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