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Ruler Postulate
The distance between any two points on the number line is the absolute value of the difference of their positions.
AB = |a – b|
a = coordinate of point A
b = coordinate of point B
Find the length of the segments:
1. AC = 2. BD =
3. AD = 4. BE =
Solution:
1. AC = 9 2. BD = 9
3. AD = 11 4. BE = 13
-8 -6 1 3 7
A B C D E
Segment Addition Postulate
If three points A, B and C are collinear and B is between A and C, then
AB + BC = AC
A B C
Example 1: If RS = 15 and ST = 9, then RT = ?
Example 2. If ST = 15 and RT = 40, then RS = ?
Solution: 1. RT = RS + ST = 15 + 9 = 24
Solution: 2. RT = RS + ST
40 = RS + 15
RS = 25
R S T
Example 3: If DT = 60, find the value of x. Then find DS and ST:
Solution: DS + ST = DT (2x – 8) + (3x – 12) = 60
5x – 20 = 60 simplify5x = 80 add 20 to each sidex = 16 divide each side by 5
DS = (2x – 8) = 2 (16) – 8 = 24ST = (3x – 12) = 3 (16) – 12 = 36
D S T
2x - 8 3x - 12
Measuring Angles
An angle is formed by two rays with the same endpoint. This common endpoint is called the vertex.
Angle can be named as: ABC, CBA, B, 1.
Measuring Angles
Angles are measured in degrees.
The measure of A is written as m A
For example: m A = 80º.
80º
Angles classified by measure
1. Acute Angle: 0º < x < 90º
2. Right Angle: x = 90º
3. Obtuse Angle: 90º < x < 180º
4. Straight Angle: x = 180º
How do we measure angles ??
Angles are measured using protractors.
Using your protractors construct the angles measuring:
1. 35 º 2. 90 º
3. 105 º 4. 180 º
Angle Addition Postulate
If point B is in the interior of AOC, then
m AOB + m BOC = m AOC
A
O C
B
Example 1: m RST = 50º and m RSW = 125º. What is m TSW?
Example 2: m DEG = 145º. What is m GEF?
Solution 1. 75º Solution 2. 35º
SR
TW
D
G
FE
Concepts of congruent segments
Segments that have the same measure are congruent segments.
Symbol of congruence
AB CD
A
B
C
D
1.7 cm1.7 cm
HW Section 1.2, pg. 18-19,
#5-8, 16-19, 21, 22, 27-29.