Download 1.1 Segments, Rays, and Distance

1.3 Segments, Rays,
and Distance
Objectives
-learn symbols for rays and segments
-Define Postulate
-Identify Ruler Postulate
-Identify Segment Addition Postulate

If we take a line and break it up into
parts, each part can be defined as a
figure.

If the part has two endpoints then it is a
segment. Segments are labeled the same
way as a line is, but the symbol displays 2
endpoints NOT ARROWS
A
A
B
C
C
A
C

Points A and C are called endpoints

In symbols it would be AC or CA

If the part has one endpoint, and the
other end extends forever it is called a
ray.
A
A
B
C
C
This would be called AC
Since A is the only endpoint, it has to be the
first letter when naming the ray
M

R
Q
Here we have what are called opposite
rays, NAME THEM.
M
T
-2
-1
V
0
1
2
3
On a number line, every point is paired with a number
and every number paired with a point. It is often
necessary to know the length of a segment on a
number line.
In this case we want to know the length of
MV, which we denote just MV. Without the
symbol above the 2 points it is showing us
that we are talking about length.

To find the length of a segment on a
number line, you simply subtract the two
endpoints values and then take the
absolute value.

Postulates (or Axioms)  these are statements
that we have to assume true because we can not
prove them.
◦ REMEMBER POSTULATES BY THEIR STATEMENT

A Little Bit of History
◦ The geometry that we are most familiar with is called
Euclidian Geometry named after the mathematician
Euclid who realized/discovered/defined 5 (some argue 6)
basic undeniable rules in which set the foundation for all
other rules in geometry. Without Euclid’s 5 absolute
truths (axioms) we would not have geometry. Authors of
today’s textbooks have divided his axioms up so that
they are easier to deal with. We will be referring to them
as postulates.
Ruler Postulate 
(1) The points on a line can be paired with
the real numbers in such a way that any
2 points can have coordinates 0 and 1

(2) Once
a coordinate system has been
chosen in this way, the distance between
any 2 points equals the absolute value of
the difference of their coordinates.
Postulate 2 Segment Addition Postulate
If B is between A and C, then

AB + BC = AC

Example.

B is between A and C, with AB=x,
BC=x+6, and AC =24.

FIND the value of x, and BC.

In geometry when 2 or more objects have
the same size and shape, they are said to
be congruent.

Congruent segments  segments that
have equal lengths.
M
A
Z
T
M
A
Z
T
To show that that AM and TZ have equal
lengths you write:
To show that AM and TZ are congruent, you
write

Midpoint  the point that divides the
segment into 2 congruent segments.

Bisector of a segment  a line,
segment, ray, or plane that intersects the
segment at its midpoint.
◦ So it is any geometric figure that cuts a
segment into 2 congruent parts.
45
W is the midpoint of XY,
Find the length of WY.
C is the midpoint of AB, Find
the length of AB.
Y is the midpoint of XZ, Find the
length of XY, YZ, XZ.

Homework
◦ Pg. 15
 #s
1,2,5-8, 15-18, 19, 24, 25, 31,33-40