- Slides: 12
Lesson 1 -2 Segments and Rays
Postulates Definition: an assumption that needs no explanation. Examples: • Through any two points there is exactly one line. • A line contains at least two points. • Through any three points, there is exactly one plane. • A plane contains at least three points.
Postulates Examples: • If two planes intersect, then the intersecting is a line. • If two points lie in a plane, then the line containing the two points lie in the same plane.
Postulates The Ruler Postulate: The points on any 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 in a number line is the absolute value of the difference of the real numbers corresponding to the points. | | PK = 3 - -2 = 5 (distance is always positive)
Between Definition: X is between A and B if AX + XB = AB AX + XB > AB
Segment Definition: two endpoints and all points between How to sketch: How to name:
The Segment Addition Postulate (This is the same as “between. ” ) Postulate: If C is between A and B, then AC + CB = AB. Example: If AC = x , CB = 2 x and AB = 12, then Find x, AC and CB. 2 x x AC + CB = AB x + 2 x = 12 3 x = 12 x = 4 AC = 4 CB = 8
Congruent Segments Definition: segments with equal lengths ~ ) ( the symbol for congruent is = Congruent segments can be marked with. . . Numbers are equal. Objects are congruent. AB: the distance from A to B ( a number ) AB: the segment AB ( an object ) Correct notation: Incorrect notation:
Midpoint Definition: a point that divides a segment into two congruent segments
Segment Bisector Definition: any object that divides a segment into two congruent parts is the bisector of the segment M
Ray Definition: 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” )
Opposite Rays Definition: ( Opposite rays must have the same “endpoint” ) opposite rays not opposite rays