Download 2.2 angle bisectors and vertical angle notes

2.2 applications­ vertical angles angle bisector ink.notebook
September 30, 2016
page 82
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2.2 apps - Vertical
Angles and Angle
Bisectors
Lesson Objectives
Standards
page 83
2.2 Applications: Vertical Angles, Angle Bisector
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2.2 applications­ vertical angles angle bisector ink.notebook
September 30, 2016
Lesson Notes
Standards
Lesson Objectives
N.Q.3
I will use limitations on geometry concepts to understand that angles and lengths cannot be negative A.CED.1 I will create an equation from a word problem and use it to solve for the missing information A.CED.1 I will create an equation from the properties of angle bisectors and use it to solve for the missing angles.
A.CED.1 I will create an equation from the properties of vertical angles and use it to solve for the missing angles. A.CED.3 I will understand that when solving equations derived from geometric concepts that the answer cannot have a negative angle or length. A.CED.3 I will demonstrate how an equation with variables on both sides, both with and without distributing can have “no solution” or an “all reals” solution
A.CED.3 I will demonstrate that distances and angles must be positive when solving geometric concepts A.CED.3 I will identify the constraints on a word problem A.REI.1 I will solve a proportion by using cross multiplication A.REI.1 I will explain each step in solving an equation with variables on both sides A.REI.3 I will solve an equation with variables on both sides with and without distribution A.REI.3 I will explain each step in solving an equation with variables on both sides Press the tabs to view details.
Lesson Notes
Standards
A.CED.1 Create equations and inequalities in one variable and use them to solve problems.
A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.
N.Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
A.REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. A.REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
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Characteristics:
My Definition:
Ray that divides
an angle into 2
equal angles
Example:
15
Angle Bisector
30
15
"=" sign goes
in the middle
2x-5
2x - 5 = 30
Counterexample:
x+
2x
2x + x
= 90
= 180
Characteristics:
My Definition:
Angles directly across
from one another
"opposite angles"
Example:
40
140
40
180
140
"=" sign goes
in the middle
Vertical Angles
2x+4
Counterexample:
90
100
2x + 4 = 100
180
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2.2 applications­ vertical angles angle bisector ink.notebook
angle bisector
30
=
2x-5
2x - 5 = 30
vertical angles
2x+4
=
100
2x + 4 = 100
midpoint
2x+4 = 28
2x+4 = 28
September 30, 2016
complementary
x+
2x
n = __________
= 90
3x = 90
Equation __________________ DE = ________
DF = ________
supplementary
2x + x
3x = 180
= 180
triangle angle sum
3x
= 180
+
x
2x
6x = 180
Angle Bisector
S
V
T
U
2.
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2.2 applications­ vertical angles angle bisector ink.notebook
3.
September 30, 2016
4.
P
40¡
J
Q
S
M
4x + 5
L
K
KM is the Û bisector of ÛJKL. R
m Û SQR = _______
If m Û JKL = 110¡, then m Û PQR = _______
m Û JKM = _______
Equation = _______________
x = _____
R
5.
6.
9n - 60
A
Q
V
Y
5n + 4 10n - 46
4n
Z
W
D
AQ bisects ÛRAD.
Equation = ___________
Equation = _____________
n = _______
n = _______
m Û RAQ = _______
m Û VWY = _______ m Û ZWV = _______ 4
2.2 applications­ vertical angles angle bisector ink.notebook
September 30, 2016
Vertical Angles
7.
P
S
40¡
R
Y
8.
109¡
V
Q
T
W
X
Z
m Û SQT = _______
m Û ZWX = ______ m Û RQT = _______
m Û XWY = ______
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2.2 applications­ vertical angles angle bisector ink.notebook
9.
September 30, 2016
B
2n + 39
E
C
10.
W
6x - 3
5n
D
V
X
F
Equation = _____________
Y
5x + 18
U
Equation = _____________
n = _______
m Û BCD = _______ x = _______
m Û YXU = ____ m Û DCF = ____ m Û ECF = ____
m Û VXU = ____, m Û WXV = ____
On Your
Whiteboards
6
2.2 applications­ vertical angles angle bisector ink.notebook
B
a)
b)
A
P
S
c)
X
100¡
32¡
4x
R
144¡0¡
144
T
U
W
AT is the angle bisector of Û BTM
Y
Û2
Û1
80¡0 OÛ3
Q
M
T
September 30, 2016
Equation = _____________
V
m Û ATM = _______ x = _______
m Û RQT = _______
m Û SQT = _______
1 Find the value of x in the d)
diagram below.
A
­2 B
­4 C
4 D
2 (6x ­ 2)
Multiple choice
On the
Worksheet
(2x + 14)
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2.2 applications­ vertical angles angle bisector ink.notebook
1.
Homework
September 30, 2016
2.
Equation __________________ Equation __________________ Answer
2
Answer
3
Answer
10
Answer
13
Answer
26
3.
4.
Answer
6
Answer
12
Answer
24
5.
Answer
20
6.
Answer
9
Answer
44
Answer
88
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2.2 applications­ vertical angles angle bisector ink.notebook
September 30, 2016
7.
8.
10.
11.
9.
12.
Equation = _____________
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2.2 applications­ vertical angles angle bisector ink.notebook
13.
September 30, 2016
Answers:
1) 4x + 1 = 6x - 5, 3, 13, 26
3) 3x - 6 = 2x, 6, 12, 24
5) 5x + 4 = 124, 24, 124, 56
7) 4x + 10 = x + 34, 8, 42, 138
9) 8x - 60 = 180, 30, 30, 150
11) 5x + 10 = 90, 16, 58, 32
13) x + 8 = 2x + 3, 5, 13, 26
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