**Angle Theorems**

**Putting the Angles in Triangle**

Parallel Lines

Angles Properties of Parallel Lines

**Geometry- Exploring Angles**

**http://www.flocabulary.com/weve-got-some-shapes/**

CAT a.k.a Complementary Angle Theory:

**2 angles whose sum = 90**

o

50

?

If we know the measurement of one angle, we can subtract the total angle by the given angle to get an answer.

a

b

c

d

a b c

= 90

o

if

bdc is 50, what does

abd equal?

o

SAT a.k.a Supplementary Angle Theorem

2 angles whose sum = 180

o

39

o

t

if pqt is 39 , what is tqr?

o

SAT is only with straight angles

CAT is only with right angles

OAT a.k.a Opposite Angle Theorem

When two line segments intersect, the opposite angles will be the same.

opposite 1

opposite 1

opposite 2

opposite 2

A

B

C

D

E

145

0

**Homework**

**Page 274, # 1-5**

Due: Tomorrow

http://www.math-play.com/Angles-Jeopardy/Classifying-Angles-Game.html

ANGLE RECAP

What's your angle? Activate your schema!

Finding Missing Angles

We use basic algebra to solve for missing angles.

Example 1: solve x

29

o

x

Steps:

1. determine the type of angle (SAT, CAT, OAT)

2. Subtract the given angle by the amount of degrees the angle should be (e.g. CAT= 90)

3. Solve until you find the value of x

29

o

x

Solve for the value of "x"

1. "x" and 29 are complementary/ CAT

2. X + 29 = 90

90 - 29 = X

90 - 29 = 61

X = 61

o

o

o

o

Example 2: solve for X and Y

X

Y

110

o

110

+ X + Y are supplementary

110

+ X + Y = 180

So, 180 - 110 = X + Y

180 - 110 = 70

* X and Y look the same size so divide 70 by 2 *

70 2 - 35

x = 35 and y = 35

o

o

o

Challenge!

A

B

C

D

E

F

G

30

15

o

o

Solve for angles CDB, EBF, FBG and GBA

X

Y

110

o

OR

SOLVE for X and Y

*** SMART NOTEBOOK**

A

B

C

Matching dashes mean same length. Therefore the angles will be the same as well!

25

o

Solution:

0

Know:

- triangles = 180

- <b and <c are the same

- <c = 25, therefore <b = 25

0

0

<A + <B + <C = 180

0

A + 25 + 25 = 180

0

A + 50 = 180

0

A = 180 -50

A = 130

0

<A = 130

0

A

B

C

D

110

20

0

0

How might we solve this?

Homework

I am a polygon. All of my sides equal 180. My insides can be made to have 5 triangles.

1

2

3

4

5

Draw a triangle with one angle that is 120 .

o

When that is completed, answer the following questions:

1. What are the measurements of the other angles?

2. What type of triangle did you draw? (Right, Acute, etc.)

Create a pentagon with equal sides.

What is the measurement of each angle in your pentagon?

Homework

Page 282 #9-13

Definition: two lines going in the same direction that never intersect

Transversal Lines

A line that crosses 2 or more lines

Transversal line

Where the lines at?

You and your partner will be given 3 minutes to find as many parallel and transversal lines in the room as possible.

*Condition* only one pair can claim a spot. If your example is taken, find another spot.

* Write your teams initial/name on your paper.

ANGLES IN LINES

Alternate Angles:

* 2 EQUAL angles.

* They form "Z" or "

"

a

b

<a = <b

In the alternate angle theory,

ANGLES IN LINES

Corresponding Angles

* 2 equal angles

* They form a "F" shape.

r

s

<r = <s

ANGLES IN LINES

Interior Angles

* 2 equal angles

* makes "c" shapes

in

terior

= inside

c

d

REMEMBER

Alternate

Angles make a "

Z

"

Corresponding

Angles make a "

F

"

Interior Angles

make a "

C

"

When you see these angles, the matching ones are the same size!

https://play.kahoot.it/#/k/45bf2cfa-f8dd-460a-8e1f-26de4fa96354

Homework

Page 287 #1-3

a

b

c

d

e

80

30

Find < ABD, <CBE, <DBE

HOMEWORK

Page 288 #7a, 8

Find x, y, z

y & 20 are "Z" pattern. So, y =20

115

y

x

z

20

115

y

x

z

20

x = 180 - (115 +20)

x = 180 - 135

x = 45

o

z = 180 - (90 + 20)

z = 180 - 110

z = 70

o

HOMEWORK

Page 305 #1 -4