7-2

7-2 Angles

Course 1

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Problem of the Day

Draw a clock face that includes the numerals 1–12. Draw two lines that do not intersect and that separate the clock face into three parts so that the sums of the numbers on each part are the same.

Problem of the Day

The measure of Jack’s angle is twice that of Amy’s and half that of Nate’s. The sum of the measures of Amy’s and Trisha’s angles is equal to the sum of the measures of Jack’s and Nate’s angles. The sum of the measures of all the angles is equal to 180°. What is the measure of each student’s angle?

Jack’s angle: 30°; Nate’s angle: 60°; Amy’s angle: 15°; Trisha’s angle: 75°

MORE WARM-UP

Use the following data set: 18, 20, 56, 47, 30, 18, 21.

1. Find the range. 2. Find the mean.

3. Find the median. 4. Find the mode.

38

Insert Lesson Title Here

30

21 18

Are you remembering your skills?

1) 1 ½ + 2 ¾ = 2) 3 ½ - 2 2/3 =

3) 3 ½ x 2 2/3 = 4) 3 ½ 2 2/3 =

5) 2.13 + 4.5 = 6) 5.13 - 4.5 =

7) 2.13 x 4.5 = 8) 2.4 .02 =

4 1/45/6

9 1/3 1 5/16

6.63 .63

9.585

120

REVIEW TEST ON THESE THURSDAY

LETS GO BACK TO 4th grade for a moment

The building blocks of geometry are points, lines, and planes.

A plane is a flat surface that plane LMN, extends without end in all plane MLN, directions. plane NLM

A plane is named by three points on the plane that are not on the same line.

M

N

L

A point is an exact location. P point P, P

A point is named by a capital letter. A line is a straight path that line AB, AB, extends without end in A B line BA, BA opposite directions.

A line is named by two points on the line.

Additional Example 1A &1B: Identifying Points, Lines, and Planes

Use the diagram to name each geometric figure.

A. three pointsM, N, and PFive points are labeled: points M, N, P, Q, and R.

B. two lines

PR and NR

You can also write RP and RN.

Q

N

P

R M

Additional Example 1C & 1D: Identifying Points, Lines, and Planes


C. a point shared by two linespoint R

D. a plane

plane QRMUse any three points in the plane that are not on the same line. Write the three points in any order.

Point R is a point on PR and NR.

Q

N

P

R M

Try This: Example 1A &1B


A. three pointsS, T, and UFive points are labeled: points S, T, U, V, and W.

B. two lines

UW and SW

You can also write WU and WS.

V

S

U W

T

Try This: Example 1C & 1D


C. a point shared by two linespoint W

D. a plane

plane VUTUse any three points in the plane that are not on the same line. Write the three points in any order.

Point W is a point on WS and WU. V

S

U W

T

A line segment is a line segment XY, XY, made of two endpoints Y line segment YX, YX and all the points between X the endpoints.

A line segment is named by its endpoints.

A ray has one endpoint. ray JK, JK From the endpoint, the ray J K extends without end in one direction only.

A ray is named by its endpoint first followed by another point on the ray.

Additional Example 2A & 2B: Identifying Line Segments and Rays

Use the diagram to give a possible name to each figure.

A. three different line segments

B. three ways to name the line

You can also write BA, CB, and CA.

AB, BC, and ACYou can also write BA, CB, and CA.

AB, BC, and AC C

A B

Additional Example 2C & 2D: Identifying Line Segments and Rays

Use the diagram to give a possible name to each figure.C. six different rays

D. another name for ray AB

A is still the endpoint. C is another point on the ray.

AB, AC, BC, CB,

CA, and BA

AC

C

A B

Try This: Example 2A & 2B


A. three different line segments

B. three ways to name the line

You can also write ED, FE, and FD.

DE, EF, and DFYou can also write ED, FE, and FD.

DE, EF, and DFF

DE

Try This: Example 2C & 2D


C. six different rays

D. another name for ray DE

D is still the endpoint. F is another point on the ray.

DE, EF, DF, FE,

FD, and ED

DF

F

DE

CAN YOU ANSWER THESE???What geometry term might you associate with each object?

1. a string on a guitar

2. a window

3. the tip of a pencil

4. a sheet of paper

line segment

plane or rectangle

point

plane or rectangle

What did the Acorn say when it grew up?

Segerson’s Warm Up

1. Draw two points. Label one point A and

the other point B.

2. Draw a line through points A and B.

3. Draw a ray with A as an endpoint and C

as a point on the ray.

4. Name all the rays in your drawing.

AB, BA, and AC

A B

C

SOME GEOMETRY JOKES

Geometry & Measurement

Chapter Five5-1

Learn to name, measure, classify, estimate, and draw angles.

How do I use this thing?

Vocabulary

anglevertexacute angleright angleobtuse anglestraight angle


A Line

A line extends in both directions for ever…never

ending!

A BAB

A Ray

A ray has one endpoint and extends without end

in one direction.

Ray identification

A ray is named by its endpoint and one other

point on the ray. AB

A B

An Angle

An angle is two rays with a common endpoint

Vertex

A vertex is the common endpoint of two rays

Angle Identification

An angle is identified by the three points…the

vertex is in the middle!A

B

C

ABCWritten like this!

CBAor

orB

Angle MeasurementAn angle is measured by

degrees and can be classified according to

their measures.

Acute Angle Right Angle Obtuse Angle Straight Angle

less than 90º is 90º more than 90º is exactly 180º

An angle is formed by two rays with a common endpoint, called the vertex. An angle can be named by its vertex or by its vertex and a point from each ray. The middle point in the name should always be the vertex.

Angles are measured in degrees. The number of degrees determines the type of angle. Use the symbol ° to show degrees: 90° means “90 degrees.”

An acute angle measures less than 90°.

A right angle measures exactly 90°.

What kind of angle is this?

An obtuse angle measures more than 90° and less than 180°.

A straight angle measures exactly 180°.


Warm UpSimplify.

1.x + 7 = 1802. 18 + x = 903. 180 = x + 434.90= x + 47

x = 173

x = 72x = 137

x = 43

Solving Subtraction Equations

Additional Example 1: Measuring an Angle with a Protractor

Use a protractor to measure the angle. Tell what type of angle it is.

• Place the center point of the protractor on the vertex of the angle.

G H

F

Additional Example 1 Continued


• Place the protractor so that ray GH passes through the 0° mark.

G H

F

• Using the scale that starts with 0° along ray GH, read the measure where ray GF crosses.



G H

F

• The measure of FGH is 120°. Write this as m FGH = 120°.



G H

F

• Since 120° > 90° and 120° < 180°, the angle is obtuse.



G H

F


Try This: Example 1


H I

G

• Place the center point of the protractor on the vertex of the angle.

Try This: Example 1 Continued


• Place the protractor so that ray HI passes through the 0° mark.

H I

G



H I

G

• Using the scale that starts with 0° along ray HI, read the measure where ray HI crosses.



H I

G

• The measure of GHI is 70°. Write this as m GHI = 70°.



H I

G

• Since 70° < 90°, the angle is acute.


Additional Example 2: Drawing an Angle with a Protractor

Use a protractor to draw an angle that measures 80°.

• Draw a ray on a sheet of paper.



• Place the center point of the protractor on the endpoint of the ray.

• Place the protractor so that the ray passes through the 0° mark.



• Make a mark at 80° above the scale on the protractor.

• Use a straightedge to draw a ray from the endpoint of the first ray through the mark you make at 80°.

Try This: Example 2


• Draw a ray on a sheet of paper.

• Place the center point of the protractor on the endpoint of the ray.

• Place the protractor so that the ray passes through the 0° mark.



• Make a mark at 45° above the scale on the protractor.

• Use a straightedge to draw a ray from the endpoint of the first ray through the mark you make at 45°.



To estimate the measure of an angle, compare it with an angle whose measure you already know. A right angle has half the measure of a straight angle. A 45° angle has half the measure of a right angle.

Now, let’s go to 6th grade!

WARM UP

• Draw a 45 degree angle without a protractor



• THEN, check to see if you were correct by using a protractor

Additional Example 3: Estimating Angle Measures

Estimate the measure of the angle, and then use a protractor to check the reasonableness of your estimate.

Let’s take a commercial break

Can think about what they

can see

Can think about what they can’t see

http://av.rds.yahoo.com/_ylt=A0oGkuHqM4NJAscApgesCqMX;_ylu=X3oDMTBxMnRhajZuBHBndANhdl9pbWdfcmVzdWx0BHNlYwNwcm9m/SIG=1243sjas2/EXP=1233421674/**http%3A//en.wikivisual.com/index.php/Psychological

That is what this was all about!

That is what this was all about!

At first glance, tell me what you see! Do you see a vase? Or do you see

something more. Look Closely!!!!









90°

About half of 90°

90 plus 45 = 135

So…..


Think: The measure of the angle is about halfway between 90° and 180°. A good estimate would be 135°.

The angle measures 131°, so the estimate is reasonable.

CAN YOU SEE THIS ONE?


Think: The measure of the angle is a little more than halfway between 0° and 90°. A good estimate would be 50°.

The angle measures 52°, so the estimate is reasonable.

How about this one

45

About 20-25

How about this one

About 165-170 or so

How about this one

85 or so?

Warm-up

Use a protractor to draw an angle with the given measure. Tell what type of angle it is.

1. 130°

2. 26°

3. Draw a right angle.

4. Is the angle shown closer to 30° or 120°?

acute

obtuse


30°

Protractor

A protractor is used to measure angles in

degrees…º

140º

Protractor

Place the Vertex of the angle in the middle….

220º

Protractor How do you know which number to use…

220º or 40º?

220º

An obtuse angle!

Protractor

A right angle!

90º

Protractor

An Acute angle!

45º

Congruent

If two angles have the same measure, they are

congruent

40º

40ºÃÃ

“Congruent” means…

“The same measure”

Find Congruent Angles!

Documents

7-2