1. 1.3 Definitions and Postulates
Honors Geometry

2. Lesson Focus
We will see how numbers can be related to points on a line. This will show the ideas of distance, length , and congruence.

3. Definitions TERM DEFINITION GRAPHIC SYMBOL LINE SEGMENT
Part of a line that is bounded by two distinct end points, and contains every point on the line between its end points 𝐴𝐵
LENGTH
The distance between two endpoints of a line
n/a
The length of 𝐴𝐵 is denoted by AB
RAY
A line that extends infinitely from an endpoint
OPPOSITE RAY
Rays with the same endpoint that extend in opposite directions
𝑃𝑄 and 𝑃𝑅 are
opposite rays

4. Guided Practice 1. Give 3 names for this line. _______________
2. Name 2 line segments:
_____________________
3. Name 2 rays:_________________
4. Name opposite rays: ______________

5. Definitions TERM DEFINTION GRAPHIC SYMBOL CONGRUENT SEGMENTS
Two segments that have equal length
MIDPOINT OF A SEGMENT
A point that divides the segment into two congruent segments
P is the midpoint of 𝐴𝐵
SEGMENT BISECTOR
A line, segment, ray, or plane that intersects the segment at its midpoint
Line l is the bisector of 𝐴𝐵 . 𝑃𝑄 and plane X also bisect 𝐴𝐵 .

6. Definitions
Point P is between points A and B. This means P must like on 𝐴𝐵 .
Postulates/Axioms are statements that are accepted without proof.

7. AB + BC = AC Postulate Postulate 2: Segment Addition Postulate
If B is between A and C, then
AB + BC = AC

8. Guided Practice
B is between A and C with AB = x. BC = x + 6 and AC = 24.
1. Find the value of x Find BC.

9. Guided Practice T is the midpoint of 𝐿𝑀 . If
LT = 4x +3 and MT= 2x + 9:
1. Evaluate for x Evaluate LT.

10. Guided Practice
3. Evaluate MT.
4. Evaluate LM.

11. NUMBER LINE
On a number line, every point is paired with a number and every number is paired with a point.

12. RULER POSTULATE
The points on a line can be paired with the real numbers in such a way that any two points can have coordinates 0 and 1.
Once a coordinate system has been chosen in this way, the distance between any two points equals the absolute value of the difference of the coordinates.

13. Finding the Length CG = 2. HK =
The distance between two points can be found by subtracting the coordinates of its endpoints:
CG =
2. HK =

14. Finding the Length

15. Guided Practice

16. Summary AB is a length. This is a number. AB = 4.
𝑅𝐺 is a ray where R is the endpoint. The arrowhead suggests that 𝑅𝐺 goes on past G.
𝑆𝑇 suggests that the line goes past S and T.