The document outlines several postulates about segments and their measures on a number line, including that the distance between two points can be found by taking the absolute value of the difference between their coordinates, and that if a point B is between points A and C, then the sum of the lengths of segments AB and BC will equal the length of segment AC. Examples are provided to demonstrate using the segment addition postulate and finding lengths of segments using given information. Key terms like congruent segments and the Pythagorean theorem are also defined.

1. 1.3 Segments & their
Measures
p. 17

2. Postulates
• Rules that are accepted as
true with having to be
proven.
• Sometimes they are called
axioms.

3. Postulate 1: Ruler post.
• The points on a line can be
matched with those on the real #
line.
• The real # that corresponds to a
point is the coordinate of the
point.
• If you find the difference between
the coordinates of 2 points, then
take the absolute value, you will
have the distance between the
points.

4. Ruler post. (continued)
A B
x1 x2
• The length of AB can be
found by x2-x1
• **The symbol for the
length of AB is AB.

5. Example: Find AB.
A B
Point A is at 1.5 and B is at 5.
So, AB = 5 - 1.5 = 3.5

6. Is Alex between Ty and Josh?
Yes!
Ty Alex Josh
No, but
How about now? why not?
In order for a point to be between 2
others, all 3 points MUST BE collinear!!

7. Post. 2: Segment Addition Post.
• If B is between A & C, then
AB + BC = AC.
• If AB + BC = AC, then B is
between A & C.
C
B
A

8. Ex: if DE=2, EF=5, and
DE=FG, find FG, DF, DG, &
EG.
D E
F
G
FG=2
DF=7
DG=9
EG=7

9. Reminders:
• Pythagorean Theorem –
a2+b2=c2
a & b are the lengths of the legs of a
right triangle and c is the length of the
hypotenuse.
• Distance formula –
( x2 − x1 ) 2
+ ( y2 − y1 )
2
(x1,y1) & (x2,y2) are the 2 points.

10. Congruent ( ≅ ) Segments
• Segments that have the same
length.
If AB & XY have the same length,
Then AB=XY,
but
AB ≅ XY
Symbol for congruent

11. Assignment