1.5 geo concepts - perimeter, segments, and angles 2017 ... Concepts Page 33 Page 34 ... x + 5 = 8...
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Transcript of 1.5 geo concepts - perimeter, segments, and angles 2017 ... Concepts Page 33 Page 34 ... x + 5 = 8...
1.5 geo concepts perimeter, segments, and angles 2017 ink.notebook
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August 31, 2017
Page 32
1.4 Two-Step Geometry Concepts
Page 33 Page 34
Page 35
StandardsLesson Objectives
Press the tabs to view details.
1.4 Using Algebra for Geometry Concepts Rules
1.5 geo concepts perimeter, segments, and angles 2017 ink.notebook
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Standards Lesson Notes
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 the properties of complementary angles and use it to solve for the missing anglesA.CED.1 I will create an equation from the properties of supplementary angles and use it to solve for the missing anglesA.CED.1 I will create an equation from the properties of triangle sum and use it to solve for the missing angles. A.CED.1 I will create an equation from the properties of segment length and use it to solve for the missing segments. A.CED.1 I will create an equation from the properties of perimeter and use it to solve for the missing segments. 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.REI.1 I will explain each step in solving a twostep equation A.REI.3 I will solve a linear 2step equation
StandardsLesson Objectives Lesson Notes
Press the tabs to view details.
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.
Examples:
MidpointThe EXACT middle of a segment
Will be told it is the midpoint. Sides are equal to each other, not a measurement.
A B C2x 20 AB = BC
A B C5 5
B is the midpoint of AC
2x = 20
Example:
Segment LengthThe pieces of a segment ADD up to the whole segment
Will usually be told what entire segment equals
Has No angles because it has No arrows
A B Cx 5
AC = 8 m
x + 5 = 8
Example:
Complementary2 angles that add up to 90
Will have a box in the corner to show it is 90
7020
70 + 20 = 90
Example:
Supplementary2 angles that add up to 180
Linear pair2 angles that make a "line" or a straight angle
150 30
150 + 30 = 180
Example:
5x + 420
5x + 24 = 90
Example:
4x + 6 30
4x + 36 = 180
1.5 geo concepts perimeter, segments, and angles 2017 ink.notebook
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August 31, 2017
Example:
Triangle SumThe sum of the measures of the interior angles of a triangle equal 180
must be the angles INSIDE the triangle
60
70
5060 + 50 + 70 = 180
3x
2x
505x + 50 = 180
Equation: _________________
x = _____
x
10 cm
Perimeter = 32 cm
1)
x = _____
MN = _____
NJ = _____
MJ = ____
Equation: ________________
Perimeter = 25 ft
2)3x - 8
2x + 4
N
M
J6x - 15
1.5 geo concepts perimeter, segments, and angles 2017 ink.notebook
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August 31, 2017
6x - 12 36 ftA B C
RV = 19 cmEquation _____________
RS = ______SV = ______
n = ________
AB = ______AC = ______
x = ________
B is the midpoint of ACEquation _____________
2n 4n - 5R S V
3) 4)
Equation: ________________
5) 6)DF
E G30
2p - 9
p = ______
m¤DEF = ______m¤DEG = ______
x = ______
m¤WYZ = ______m¤ZYV = ______
WZ
Y V4x
2x + 6
Equation: ________________
1.5 geo concepts perimeter, segments, and angles 2017 ink.notebook
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August 31, 2017
Equation: _________________
x = __________
m¤PQS = ______
m¤SQR = _______
3x + 15 7x + 45
S
P Q R
Equation: _________________
x = __________
m¤UVW = ______
m¤WVX = _______
2x + 6 3x + 4
W
U V X
7) 8)
6x + 4
3x + 1 5x
A
BC
x = _______ m¤A = _____
m¤B = ____ m¤C = ____
Equation ________________ 9)
1.5 geo concepts perimeter, segments, and angles 2017 ink.notebook
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August 31, 2017
On Your Whiteboards Pull
Pull 2x + 17 = 25
PullPull
BC = 8 m
7 m
10 m
2x
Equation: _________________
x = _____
Perimeter = 25 m
a)
3x xM N O
MO = 20 in
x = ______
MN = _____
NO = _____
Equation: _________________
b)
On the Worksheet
1.5 geo concepts perimeter, segments, and angles 2017 ink.notebook
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Homework
3x - 6
2x TR
S
x
x = _____
RS = _____
RT = _____
ST = ____
Equation: ________________
Perimeter = 84 in
1.
4x - 3
2x + 5T
V
U
7x - 12
x = _____
TU = _____
UV = _____
TV = ____
Equation: ________________
Perimeter = 68 m
2.
x = _____
UV = _____
VX = _____
Equation: ________________
Perimeter = 62 in
3.
2x
x + 10
Z
U V
W
1.5 geo concepts perimeter, segments, and angles 2017 ink.notebook
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August 31, 2017
6x - 8 10xN B Q
NQ = 56 km
x = _____
NB = _____
BQ = _____
Equation: ________________
4. 73 in 6x + 1A P V
x = _____
PV = _____
AV = _____
Equation: ________________
5.
P is the midpoint of AV
4x + 8 24 inM Y Z
WY = 150 cm
x = _____
MY = _____
MZ = _____
Equation: ________________
6. 8x - 12 x W Z Y
x = _____
WZ = _____
Equation: ________________
7.
Y is the midpoint of MZ
Equation: ________________
8) R
T
S P3n
7n + 10
n = ______
m¤RST = ______m¤TSP = ______
9)
x = ______
m¤WYZ = ______m¤ZYV = ______
WZ
Y Vx + 14
2x - 5
Equation: ________________
Equation: _________________
x = __________
m¤PQS = ______
m¤SQR = _______
8x 4x + 12
S
P Q R
Equation: _________________
x = __________
m¤UVW = ______
m¤WVX = _______
4x + 13 2x + 5
W
U V X
10) 11)
1.5 geo concepts perimeter, segments, and angles 2017 ink.notebook
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August 31, 2017
11x + 4
5x - 3 2x - 1
M
PA
x = __________
m¤M = _______
m¤P = ______
Equation ________________
12)
5x + 39
3x + 50 3x - 8
T
RS
x = __________
m¤S = _______
m¤R = ______
Equation ________________
13)Answers: 1) x = 15, 39 in, 30 in, 15 in 3) x = 7, 17 in, 14 in 5) x = 12, 73 in, 146 in 7) x = 18, 132 cm 9) x = 27, 49, 41 11) x = 27, 121, 59 13) x = 9, 77, 19
Extra Practice
True False
Perimeter measures the distance around a figure or area.
1 True or False
1.5 geo concepts perimeter, segments, and angles 2017 ink.notebook
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August 31, 2017
2 What is the formula for finding the perimeter of a rectangle?
A P = l + w
B P = 2(l + w)
C P = (l + w)/2
D P = l x w
Multiple choiceThe width of a rectangle is 3 cm less than its length. The perimeter is 18 cm. What is the length?
3 Numeric
The length of a rectangle is 4 in. more than the width. The perimeter is 20 in. What is the width?
4 Numeric
The length of a rectangle is triple the width. The perimeter is 48. What are the dimensions?
5
4 5 by 15
3 6 by 18
2 7 by 21
1 4 by 12
Sorting
1.5 geo concepts perimeter, segments, and angles 2017 ink.notebook
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August 31, 2017
7x + 5x = 9012x = 90x = 7.5The larger angle is 52.5oThe smaller angle is 37.5o
5x + x = 906x = 90x = 15The smaller angle is 15oThe larger angle is 75o
Word problems
Two angles are complementary. The larger angle is 5 times greater than the smaller angle. Find the measure of the 2 angles.
Two angles are complementary. The measure of the anglesare in a ratio of 7:5. Find the measure of the angles.
8x + x = 1809x = 180x = 20The smaller angle is 20oThe larger angle is 160o
Word problems
Two angles are supplementary. The larger angle is 8 times greater than the smaller angle. Find the measure of the 2 angles.
The measure of the supplement of an angle is 10o more thanfour times the original angle. Find the measure of the two angles.
Equation: ________________
9) DF
E G3p +2
2p +8
p = ______
m¤DEF = ______m¤DEG = ______