Transcript 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
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.
.
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