1. Lesson 1-2
Segments and Rays

2. 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.

3. 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.

4. 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.
| | = 5
PK =
(distance is always positive)

5. Between AX + XB = AB AX + XB > AB
Definition: X is between A and B if AX + XB = AB.
AX + XB = AB
AX + XB > AB

6. Segment Definition: two endpoints and all points between
How to sketch:
How to name:

7. 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 x = 12
3x = 12
x = 4
x = 4
AC = 4
CB = 8

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:

9. Midpoint Definition: a point that divides a segment into two
congruent segments

10. Segment Bisector Definition:
any object that divides a segment into two congruent parts is the bisector of the segment M

11. 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” )

12. Opposite Rays Definition:
( Opposite rays must have the same “endpoint” )
opposite rays
not opposite rays