1.3/1.4 Postulates and
Measuring Segments and
Angles
Chapter 1 Tools of Geometry
Postulates

Are statements accepted as true without
proof

They are considered self-evident

They are accepted on faith alone.
Postulate 1-5
Ruler Postulate
The distance between any two points is the absolute
value of the difference of the corresponding
numbers (on a number line or ruler)
Congruent Segments: two segments with the same
length
Comparing Segment Lengths
Postulate 1-6
Segment Addition Postulate
If three points A, B, and C are collinear and B is
between A and C, then AB + BC = AC
C
B
A
Using the Segment Addition Postulate
If DT = 60, find the value of x. Then find DS and ST.
2x - 8
D
3x - 12
S
T
Using the Segment Addition Postulate
If EG = 100, find the value of x. Then find EF and FG.
4x - 20
E
2x + 30
F
G
Midpoint: a point that divides the segment into two
equal parts
A
B
B is the midpoint, so AB = BC
C
Finding Lengths
C is the midpoint of AB. Find AC, CB, and AB.
3x – 4
2x + 1
A
C
B
Z is the midpoint of XY, and XY = 27. Find XZ.
27
X
Z
Y
Angle: formed by two rays with the same endpoint
The endpoint is called the vertex
Can be named by the vertex, by three letters
with the vertex in the center, or by a number
A
B
<ABC
<CBA
<B
<1
1
C
*Look at examples in your notes
Postulate 1-7
Protractor Postulate
You can use a protractor to measure an angle.
*Look in book on page 28
Acute angle
< 90°
Right Angle
= 90°
Obtuse Angle
> 90° but < 180°
(90° < x < 180°)
*Example 5 on pg 28
Straight Angle
= 180°
Postulate 1-8
Angle Addition Postulate
If point B lies in the interior of <AOC, then m<AOB +
m<BOC = m<AOC
A
B
O
C
If <AOC is a straight angle, then m<AOB + m<BOC
= 180
B
A
O
C
Using Angle Addition Postulate
What is m<TSW if m<RST = 50 and m<RSW = 125?
T
x
50
R
S
W
Using The Angle Addition Postulate
If m<DEG = 145, find m<GEF.
G
145
D
x
E
F
Congruent Angles: Angles with the same measure
Homework
Problems # 1-9 on worksheet #2
Segment and Angle Addition