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. | 3 - -2 | = 5 PK = (distance is always positive)

Between AX + XB = AB AX + XB > AB Definition: X is between A and B if AX + XB = AB. 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 = 2x and AB = 12, then Find x, AC and CB. 2x x 12 AC + CB = AB x + 2x = 12 3x = 12 x = 4 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 : 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