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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.