complementary, supplementary, and vertical...

1. Measuring Angles (4).notebook

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IWBAT estimate, classify, measure and draw acute, obtuse, right, straight, 180+, complementary, supplementary, and vertical angles.


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Angles are measured in degrees!


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Angle Types

NAME DEFINITION EXAMPLE

Acute angle angle less than 90

Right angle angle equal to 90

Obtuse angle angle between 90 and 180

Straight angle angle equal to 180

Reflex angle angle greater than 180, less than 360

Please Create a Vocabulary section for unit 3

PICTURE


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Angle NotationB

Symbols: ∠BRead: "angle B"

vertex

I do


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Angle NotationB

Symbols: ∠B, ∠ABC, OR ∠CBARead: "angle B," "angle ABC, " or "angle CBA"

It can also look like this!

A

C

I do


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Angle NotationW

X

Y

Z

What color is angle WXY?What color is angle YXZ?What color is angle ZXW?


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What is a protractor?A protractor is a tool that helps us measure angles.


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Measuring angles correctly is importantbecause it helps us build things like this:


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Not this:


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Drawing Angles Draw each angle type in your notes:

acute angle

right angle

obtuse angle

straight angle

reflex angle


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Step 1: Determine if the angle is acute, obtuse, right, or straight before using the protractor. Give yourself an estimate.

Write down these steps!

Measuring an Angle


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Acute, Obtuse, Right, or Straight?


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We can estimate the measure of an angle by visually comparing it to a 90° angle and a 180° angle

90° 180°


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Which is the best estimate of the measure of this angle?

1. 155°2. 85°3. 45°4. 25°

Check for Understanding


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Step 2: Place the Center Mark of the Protractor on the Vertex of the Angle (where the two lines meet)

Measuring an Angle


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Step 3: Rotate the zeroedge so that it ison top of the horizontal line


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Step 4: Read the angle measurement, comparewith your estimate, and record.


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Putting it all together...


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What about this???


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Independent PracticeBefore you measure each angle:

1.) Classify each angle as acute/right/obtuse/straight/reflex2.) ESTIMATE the angle measure

Only THEN can you measure the angle using your protractor


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DOL

1. Correctly name each angle measurement:

a. 9°

b. 250°

2. Measure problems 4,5,6 in your independent practice and label correctly.

c. 90°

d. 180°

e. 88°


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Acute angles

Using your ruler, draw AB 64 mm long

Using your protractor, mark a 38 angle off of vertex A

Using your ruler, draw AC 8.8 cm long

Pass to your shoulder partner and have them check your work


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64 mm = 6.4 cm38

8.8 cm

= 88

mm

A

B

C

What are the 3 names we could call this angle?


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Right Angles

Draw XY 2 cm long. Then draw YZ 1.5 cm long perpendicular to XY.

Complete XYZ by drawing XZ.

How long is XZ?

Mark the right angle with the appropriate sign


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X Y

Z

2 cm

1.5 cm2.5 cm

Perpendicular lines make right angles


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Obtuse Angles

Create a triangle that includes 1 obtuse angle.

What conjecture can you make about the other angles?


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Straight Angles ‐ straight lines

Straight lines make a half circle. How many degrees are in a straight angle?


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Straight Angles

A B C

D

If the m ABD is 127 , name and find the measure of the acute angle


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Straight Angles with a triangle

A B C

D

You now know the m DBCAngle BDC is 47.5Can you calculate the measure of angle DCB?


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Find the measures of all the angles

38E F

G

61


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Circle Angles add up to 360 degrees

Find the missing angles

1351

23


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Interesting,

All 3 angles in a triangles add up to 180 degrees.

All straight lines measure 180 degrees.

All circle measure 360 degrees.

All 4 angles in a quadrilateral add up to 360.


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Summary:

Right angles = 90 degrees.

Straight lines = 180 degrees.

If 2 angles create a right angle or a straight line, they are given special names.


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A

B

C

D

E F

G

H

∠ABC + ∠CBD = 90° ∠EFG + ∠GFH = 180°


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Complementary Angles

1. What is the measure of angle B?

63B

2. What is the complement of an angle that measures 72 degrees?


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1234


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Supplementary Angles

1. What is the measure of angle B?

145.5B

2. What is the supplement of an angle that measures 72 degrees?


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1234


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Alternate Interior

Must have 2 parallel linesMust have a transversal

tran

sver

sal

130

130

130

13050

50

50

50


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Alternate Exterior

Must have 2 parallel linesMust have a transversal

tran

sver

sal

130

130

130

13050

50

50

50


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a.)

a.) name a pair of vertical angles

b.) name a pair of supplementary angles

d.) name a pair of alternate exterior angles


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Activity

There are 10 objects around the room with marked angles.

It is you and your partner's job to find the angle measures using your protractors.


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Find the measure of each missing angle

1 23 4

5 67 137

If we are given 2 parallel lines and a transversal, 8 angles are created. We only need to be given 1 measurement. The rules of geometry allow us to calculate all the remaining angles.


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Do you think these lines are parallel?

mathematically prove your answer

52.7

128.3


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Point!Which way is vertical

from you?


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1 2

3

1 and 3 are congruent: alternate interior1 and 2 are supplementaryTherfore, 2 and 3 are supplementary


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Check for Understanding

1. Acute or obtuse? 144

2. A pair of angles that are 25.5 and 154.5 are called what type of angles?

3. Find the measure of angle x and y


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Vertical Angles

135

13545

45

Vertical angles are across from each otherVertical angles are congruent (the same)Do you see the circle?


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Extension:

If there are 4 angles at a point and they are in the ratio of 3:4:5:6, what is the size of the smallest angle?

a. 18 c. 54

b. 20 d. 60


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1 2

3

Do you see the trapezoid?

Extension


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DOL1.) What is wrong with this picture?

135 55

45

55

2a.)

2b.) If angle 2 is 126 degrees, how much do angles 1, 3, 4, and 5 add up to?

3.) Find the measurement of all the remaining angles. A

BCD68°


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