Lesson 1-2: Segments and Rays

Lesson 1-2: Segments and Rays Postulates Definition: An assumption that needs no explanation. Examples: La intersección de dos líneas es un punto line. La intersección de dos líneas es un punto two points. La intersección de dos líneas es un punto, there is exactly one plane. La intersección de dos líneas es un punto points. Lesson 1-2: Segments and Rays

Lesson 1-2: Segments and Rays Postulates Examples: La intersección de dos líneas es un punto If two points lie in a plane, then the line containing the two points lie in the same La intersección de dos líneas es un punto. Lesson 1-2: Segments and Rays

Lesson 1-2: Segments and Rays The Ruler Postulate The 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

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 = | 3 - -2 | = 5 Remember : Distance is always positive Lesson 1-2: Segments and Rays

Lesson 1-2: Segments and Rays Between Definition: X is between A and B if AX + XB = AB. AX + XB = AB AX + XB > AB Lesson 1-2: Segments and Rays

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

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. 2x x 12 Step 1: Draw a figure Step 2: Label fig. with given info. AC + CB = AB x + 2x = 12 3x = 12 x = 4 Step 3: Write an equation x = 4 AC = 4 CB = 8 Step 4: Solve and find all the answers Lesson 1-2: Segments and Rays

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

Lesson 1-2: Segments and Rays Midpoint Definition: A point that divides a segment into two congruent segments Formulas: On a number line, the coordinate of the midpoint of a segment whose endpoints have coordinates a and b is . In a coordinate plane, the coordinates of the midpoint of a segment whose endpoints have coordinates and is . Lesson 1-2: Segments and Rays

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

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

Lesson 1-2: Segments and Rays Definition: RA : RA and all points Y such that A 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

Lesson 1-2: Segments and Rays Opposite Rays Definition: If A is between X and Y, AX and AY are opposite rays. ( Opposite rays must have the same “endpoint” ) opposite rays not opposite rays Lesson 1-2: Segments and Rays