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Geometry- Exploring Angles

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Ms. Norville

on 16 December 2015

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Transcript of Geometry- Exploring Angles

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
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