Lesson 1.5: Measuring Segments
Lesson 1.6a: Measuring Angles
Absolute Value
A number’s distance from zero. REMEMBER: DISTANCE IS
ALWAYS POSITIVE!
9 
3
8 3 
0
Postulate 1-5
The Ruler Postulate: The distance between points on a number line
(or on a ruler) is the absolute value of their difference.
Remember: Distance is always positive!
Note: The distance between A and B, or the length of AB , is written
as AB (no line above the letters!)
Ex: 1. Find DE
2. Find CE
3. Find AC
Congruence
Congruent Segments: Segments that have the same length
If AB = BC, then AB  BC
Ex: Are AB and BC congruent?
(Check if AB = BC)
Do you see any other pairs of
congruent segments?
Postulate 1-6
Segment Addition Postulate: If 3 points A,
B, and C are collinear and B is between A
and C, then AB + BC = AC
A
B
C
Example: If TV = 46, find the value of x. Then find the values of
TU and UV.
3x - 2
T
4x + 6
U
V
Postulate 1-6
Segment Addition Postulate: If 3 points A,
B, and C are collinear and B is between A
and C, then AB + BC = AC
A
B
C
Example: Q is the midpoint of PR . Find PQ, QR, and PR.
2x + 14
P
5x + 2
Q
R
Angles
Angle: An angle is formed by two rays with the same endpoint.
T
B
Name:
1
K
Name:
C
J
2
P
3
R
Types of Angles
Acute Angle: less than 90°
Obtuse Angle: more than 90°
Right Angle: Exactly 90°
Straight Angle: exactly 180°
Postulate 1-7
Protractor Postulate: O is a point with
opposite rays called OA and OB going to the
left and right. Any ray drawn up from O
creates and angle with a measure between
0 and 180.
Let’s talk
about
measuring
angles with a
protractor…
180
0
180
0
Postulate 1 - 8
Angle
AngleAddition
AdditionPostulate:
Postulate:
Ex: What is mTSW if
mRST  40 and
mRSW  115 ?
Ex. If mDEG  130, find mGEF
Lesson 1.5: Measuring Segments
Lesson 1.6a: Measuring Angles
HW: p.33 #6-14 even, 20-23, 35-37
p.40 #1-8, 13-14
THT: Can do #1-7, 9-10, 13-16
Terms: acute angle, obtuse angle, right angle, straight
angle, congruence