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Chapter 1: Essentials of Geometry
Section 2: Use Segments and Congruence
Key terms:
1. Postulate/ Axiom (p. 9)
4. Between (p. 10)
2. Coordinate (p. 9)
5. Congruent segments (p. 11)
3. Distance (p. 9)
WHAT IS A POSTULATE OR AXIOM?
A rule that is accepted without proof!
Postulate 1: ruler postulate
The points on a line can be matched one to one with real numbers.
names of points
A
x1
B
coordinates of points
x2
The real number that corresponds with a point is called the COORDINATE.
A
x1
AB
AB= I x2 – x1I
B
x2
Postulate 1 continued…
The DISTANCE BETWEEN TWO POINTS ON A LINE is the absolute value of the
difference of the coordinates of the points.
Example: The “distance between points A and B” is the same thing as “AB” and/ or
the “length of AB”.
Example 1:
Example 2:
When three points are COLLINEAR, the point in the middle is BETWEEN the other
two.
B
A
B
C
Point B is between points A and C.
A
C
Point B is NOT between points A and C.
Postulate 2: segment addition postulate
If B is between A and C, then AB + BC – AC.
If AB + BC – AC, then B is between A and C.
Example 1:
Example 2:
Review:
Examples of coordinate pairs (x, y) are (-3, 2) and (3, 2).
To find the horizontal length (difference) between the
two points use absolute value. AB = I 3 – (- 3 ) I = 6
Additional Examples:
Example 1:
Example 2: