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Transcript 
Section 1.4
Measuring Segments and
Angles
Ms. Olifer
Geometry
OBJECTIVES
SWBAT:
 Find the lengths of segments
 Find the measures of angles
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).
Distance  | a  b |
Congruent Segments: two segments with the
same length.
Geometry vs Algebra

Segments are Congruent

Symbol [  ]
AB  CD


1  2
Lengths of segments are equal.



Symbol [ = ]
AB = CD
m1 = m2
Comparing Segment Lengths

Look in book for Example 1, pg 26
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
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.
X
Z
27
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 example 4 in the book, pg 27
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.
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