Do Now: Find the distance between the following

points:(12,12) and (-3,1). Then

find the distance between (1,-9) and (6, -6)

Objective

SWBAT name, measure, and classify angles.

What is an angle?

•An angle is formed by two rays with a common endpoint.•The common endpoint is called a vertex.•The two rays are called the sides of an angle

CFU #1

What is a vertex?A. A sideB. A rayC. An endpoint

How do we name an angle?

•Angles are named by naming a point on one side, then the vertex, then a point on the other side.

It doesn’t matter which side you start with as long as the vertex is in the

middle!

CFU #2

How many angles can you name in the picture below?

Protractor Postulate

•Angles are measured with something called a protractor. •A protractor is a measuring device that measures how “open” an angle is. •Angles are measured in degrees, and labeled with a ⁰ symbol.

How to use a protractor

What is the

measure of the angle

shown ?

Classifying Angles

•Angles that measure less than 90⁰ are called acute angles.•Angles that measure exactly 90⁰ are called right

angles.•Angles that measure more than 90⁰ are called obtuse

angles.•Angles that measure exactly 180 ⁰ are called straight

angles.

Is it acute, right, obtuse, or straight?

Angle Addition Postulate

First, let’s recall some previous information from last week….

We discussed the Segment Addition Postulate, which stated that we could add the lengths of adjacent segments together to get the length of an entire segment.

For example:

JK + KL = JL

If you know that JK = 7 and KL = 4, then you can conclude that JL = 11.

The Angle Addition Postulate is very similar, yet applies to angles. It allows us to add the measures of adjacent angles together to find the measure of a bigger angle…

J K L

Angle Addition Postulate

50°65°

AB

CO

If B lies on the interior of ÐAOC, then mÐAOB + mÐBOC = mÐAOC.

mÐAOC = 115°

Example 1G

H J

K

Given: mÐGHK = 95 mÐGHJ = 114.

Find: mÐKHJ.

The Angle Addition Postulate tells us:mÐGHK + mÐKHJ = mÐGHJ

95 + mÐKHJ = 114

mÐKHJ = 19.

95°

114°

19°

Plug in what you

know.Solve.

R

S T

V

Given:mÐRSV = x + 5mÐVST = 3x - 9mÐRST = 68

Find x.

mÐRSV + mÐVST = mÐRST

x + 5 + 3x – 9 = 68

4x- 4 = 68

4x = 72

x = 18

Set up an equation using the Angle Addition Postulate.

Plug in what you

know.Solve.

Extension: Now that you know x = 18, find mÐRSV and mÐVST.

mÐRSV = x + 5mÐRSV = 18 + 5 = 23

mÐVST = 3x - 9mÐVST = 3(18) – 9 = 45

Check:mÐRSV + mÐVST = mÐRST23 + 45 = 68

B

QD

CmÐBQC = x – 7 mÐCQD = 2x – 1 mÐBQD = 2x + 34

Find x, mÐBQC, mÐCQD, mÐBQD.

mÐBQC + mÐCQD = mÐBQD

3x – 8 = 2x + 34

x – 7 + 2x – 1 = 2x + 34

x – 8 = 34x = 42

mÐBQC = 35

mÐCQD = 83

mÐBQD = 118

x = 42

mÐBQC = x – 7mÐBQC = 42 – 7 = 35

mÐCQD = 2x – 1mÐCQD = 2(42) – 1 = 83

mÐBQD = 2x + 34mÐBQD = 2(42) + 34 = 118

Check:mÐBQC + mÐCQD = mÐBQD35 + 83 = 118

Guided Practice

Complete questions 1 through 8 in groups. Be prepared to review the questions in front of the class.

Independent Practice

On a sheet of loose leaf paper. Complete questions 9 through 12 using the statement/ reason method. Your final answers should be boxed and the value of each angle should be clearly marked. This portion of the class should be silent. If you have a question that you must ask a neighbor, please be sure to whisper.