1. Lesson 1-2: Segments and Rays

2. 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

3. 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

4. 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

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

6. 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

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. 2x x 12
Step 1: Draw a figure
Step 2: Label fig. with given info.
AC + CB = AB
x x = 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

9. 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

10. 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

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 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

13. 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

14. 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