Investigating Geometry Online Homework 1-2 Segments And Rays Answers

Presentation on theme: "Lesson 1-2: Segments and Rays"— Presentation transcript:

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

Construct intersecting Chords at the following degrees:

22.5, 30, 37.5, 45, 60, 75, 82.5, 90, 97.5, 105

Steps:

(1) double the target angle (2x)

(2) construct an arc less than this 2x

     Lable the endpoints of this arc

(3) Construct another separate arc equal to the remaining measure

     Lable the endpoints of this arc

(4) make the two Chord such that they interest the two arcs

     Lable the point of intersection 

(5) Make a statement showing that 1/2 times the sume of the two arcs equals your target angle

 

Example: Tageet arc is 22.5 degrees

(1) 2*22.5=45

(2) 30 is less than 45, construct it and lable it AB

(3) 15 is the rest of the 45, construct it and lable it CD

(4) Connect the points AC and BD to interect at point "X"

(5) Make the following statement (with angle and arc symbols)

      m
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