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2.2 Applications: Vertical Angles, Angle Bisector
Name ______________________
Learning Objective: N.Q.3
I will use limitations on geometry concepts to understand that angles and lengths
cannot be negative
I will create an equation from a word problem and use it to solve for the missing information
I will create an equation from the properties of angle bisectors and use it to solve for the missing
angles.
I will create an equation from the properties of vertical angles and use it to solve for the missing
angles.
I will understand that when solving equations derived from geometric concepts that the answer
cannot have a negative angle or length.
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
I will demonstrate that distances and angles must be positive when solving geometric concepts
I will identify the constraints on a word problem
I will solve a proportion by using cross multiplication
I will explain each step in solving an equation with variables on both sides
I will solve an equation with variables on both sides with and without distribution
I will explain each step in solving an equation with variables on both sides
A.CED.1
A.CED.1
A.CED.1
A.CED.3
A.CED.3
A.CED.3
A.CED.3
A.REI.1
A.REI.1
A.REI.3
A.REI.3
Write and solve an equation by showing all work. Then find the missing information.
5x
6x - 5
2x + 6
4x + 1
1.
2.
J
M
K
L
G
H
H is the midpoint of GJ
Equation ________________
L is the midpoint of KM
Equation _________________
x = ________
x = _______
GH = ______
KL = ______
GJ = _______
KM = ______
H
N
3.
4.
3x – 6
J
6n – 10
L
2x
P
M
4n + 8
R
K
Equation = _____________
Equation = _____________
x = _______
n = _______
m  HLJ = _______
m  NPM = _______
m  HLK = _______
m  NPR = _______
P
5.
S
6.
E
B
124
6x – 3
Q
5x + 4
T
R
C
7.
W
x + 34
V
5x + 8
X
F
D
Y
4x + 10
U
Equation = _____________
Equation = _____________
Equation = _____________
x = _______
x = _______
x = _______
m  RQT = _______
m  BCD = _______
m  YXU = _______
m  SQT = _______
m  DCF = _______
m  VXU = _______
8.
9.
10.
M
A
x+6
2x – 4
N
7x – 60
N
J
4x – 10
Perimeter = 20 m
J
3x
x
L
7x – 40
B
M
2x + 4
C
Equation = _____________
Equation = ____________
x = _________
x = __________
x = ________
MN = _______
m  NLM = _______
m  A = _______
NJ = _______ MJ = _____
m  JLN = _______
m  C = _______
Equation = _____________
11.
B
Y
12.
3x + 10
D
V
6n + 2
13.
9n – 7
3 + 2x
x+8
Z
A
M
B
2x
C
E
W
M is the midpoint of AB
Equation = _____________
Equation = _____________
Equation = _____________
x = _______
n = __________
x = ________
m  BCD = ________
m  VWY = _______
AM = _______
m  DCE= _______
m  VWZ = _______
AB = _______
Answers:1) 4x + 1 = 6x - 5, 3, 13, 26 3) 3x - 6 = 2x, 6, 12, 24 5) 5x + 4 = 124, 24, 124, 56
9) 8x - 60 = 180, 30, 30, 150 11) 5x + 10 = 90, 16, 58, 32 13) x + 8 = 2x + 3, 5, 13, 26
7) 4x + 10 = x + 34, 8, 42, 138
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