do now. ruler postulate the distance between any two points on the number line is the absolute value...
TRANSCRIPT
DO NOW
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.