Homework 1-2 Segments And Rays Answers

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1 Lesson 1-2: Segments and Rays

2 Lesson 1-2: 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 1-2: Segments and Rays

3 Lesson 1-2: Segments and Rays
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 1-2: Segments and Rays

4 Lesson 1-2: Segments and Rays
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 1-2: 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 1-2: Segments and Rays

6 Lesson 1-2: Segments and Rays
BetweenDefinition: X is between A and B if AX + XB = AB.AX + XB = ABAX + XB > ABLesson 1-2: Segments and Rays

7 Lesson 1-2: Segments and Rays
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 1-2: 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 1-2: Segments and Rays

9 Lesson 1-2: Segments and Rays
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 1-2: Segments and Rays

10 Lesson 1-2: Segments and Rays
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 1-2: 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 1-2: Segments and Rays

12 Lesson 1-2: Segments and Rays
Segment BisectorDefinition:Any segment, line or plane that divides a segment into two congruent parts is called segment bisector.Lesson 1-2: Segments and Rays

13 Lesson 1-2: Segments and Rays
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 1-2: Segments and Rays

14 Lesson 1-2: Segments and Rays
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 1-2: Segments and Rays


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.

 Applet Directions 1 Close 
  1. Construct segment EF so that AB + CD = EF.

  2. Using the cirlce tool , construct a circle with radius AB and center E.
 Applet Directions 2 Close 
  1. Using the intersection tool , click on the intersection of the circle with the dotted ray.

  2. Construct a second circle with radius CD and center on the intersection found in step 1.

  3. Construct a line segment from point E to the intersection of the dotted line and the second circle.

  Other Web Sites Close 
  1. General TerminolgyMath.com: Steps 1 through 3 (1-First Glance, 2-In Depth, 3-Examples) are similar to a textbook while step 4 (Workout) is an online multiple choice "quiz" with instant feedback.
  2. Glencoe: On Line Quiz

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