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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1.4 Two-Step Geometry Concepts

Page 33 Page 34

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StandardsLesson Objectives

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1.4 Using Algebra for Geometry Concepts Rules


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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

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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


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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


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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: ________________


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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)


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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


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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


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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)


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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


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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


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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 = ______

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...