### 1.2 and 1.3 Segment and Segment Congruence with midpoint

```Points, Lines, and Planes
Section 1.2 Segments and Congruence
Section 1.3 Use Midpoint and Distance
Formulas
Ruler Postulate
•The points on a line can be matched
one to one with the real numbers.
•There are an infinite number of points
on a line and an infinite number of real
numbers.
•The real number that corresponds to
the point is the coordinate of the point.
AB
The distance between point A and point B.
The length of AB.
A
B
.
.
12
AB = 12
•AB means “the distance
between point A and Point B”.
(number)
•AB means “line AB”. (figure)
•AB means “segment AB”.
(figure)
•AB means “ray AB”. (figure)
Distance Formulas
Number Line
• Absolute value of the
difference between the
coordinates
A
.
Coordinate Plane
• Distance Formula
B
.
√
You can only use the word “between” if all
three points are collinear.
.
A
.
.
B
C
B is between A and C
.
D
.E
.
F
E is not between D and F
If B is between A and C, then AB + BC = AC.
If AB + BC = AC, then B is between A and C.
.
A
5
.
12
B
17
.C
Congruent Segments
Line segments that are the same length.
AB = CD
The lengths are equal.
The Segments are congruent.
.A
.B
.C
.D
Midpoint
The point that divides the segment into two
congruent segments.
A segment has exactly one midpoint.
.A
.M
.B
M is the midpoint of AB.
Segment Bisector
•A point, ray, line, line segment , or
plane that intersects a segment at
its midpoint.
•A segment can have an infinite
number of bisectors.
.
.
.
Midpoint Formula
Number Line
The coordinates of the
midpoint of a segment
whose endpoints have
coordinates a and b is
Coordinate Plane
```