# 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

## 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.

 Applet Directions 1 Close Construct segment EF so that AB + CD = EF.Using the cirlce tool , construct a circle with radius AB and center E.
 Applet Directions 2 Close Using the intersection tool , click on the intersection of the circle with the dotted ray.Construct a second circle with radius CD and center on the intersection found in step 1.Construct a line segment from point E to the intersection of the dotted line and the second circle.

 Other Web Sites Close 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.Glencoe: On Line Quiz