Geometry Week of June 8th - June 15th Grades 9 and 10_Geom_Week_June… · Geometry Week of June 8th - June 15th S u b mi s s i on : P l e a s e s ubm i t a l l of *your a s s i gnm

Geometry Week of June 8th - June 15th

Submission: Please submit all of *your assignments by uploading to the corresponding Microsoft Teams assignment.* Guided Notes: Attached to this page are guided notes for you to fill in for each of the respective lessons for the week. The guided notes are meant to go along with the examples from each lesson in the textbook similarly to how we would take notes in class. You do not need to submit these back to me but are encouraged to use them as a resource for yourself to refer back to. Homework: The lessons homework is also expected to be completed within two days of the video lesson. You will be responsible for completing the homework assignment for that lesson and submitting it via email. Grading: Homework assignments will be graded as either Non Accuracy or Accuracy Homework assignments. IXL and lesson practice will be graded as classwork/participation grade. ALL work must be shown, and each problem must be attempted in order to receive full credit. Note: Study guide 22 was attached to last week’s packet.

*NEW* Last day for missing work is Wednesday June 17th!!!

*NEW* Attached is the Final Exam Study Guide, it is due on June 17th!! Assignments: Monday: Watch video on Lesson 118 and Lesson Practice 118 (10 points) and Lesson 118 HW *CP complete attached worksheet; Honors, complete book problems 1-30* (10 points) submit by 11:59pm on Wednesday 6/10. Tuesday: Watch video on Lesson 119 and Lesson Practice 119 (10 points) and Lesson 119 HW *CP complete attached worksheet; Honors, complete book problems 1-30* (10 points) submit by 11:59pm on Thursday 6/11. Wednesday: Watch video on Lesson 120 and Lesson Practice 120 (10 points) and Lesson 120 HW *CP complete attached worksheet; Honors, complete book problems 1-30* (10 points) submit by 11:59pm on Friday 6/12. Thursday: Study Guide 22 is due today (10 points) Submit by 11:59 on Thursday 6/11 by 11:59 pm Friday: Complete Accuracy 22 assignment on Microsoft teams. The assignment is based off of study guide 21 (48 points) Submit by 11:59 on Monday 6/15. Collaboration is not allowed. Collaboration - to work jointly with others or together especially in an intellectual endeavor. When collaboration takes place, all students must demonstrate understanding of the new material.

Name:________________________________________ Period:___________ Date:_________________

Lesson 118: Finding Areas of Polygons using Matrices Determinant of an mX2 Matrix

1. Calculate the determinant of A = [6 19 23 1

].

The area of a polygon on a coordinate plane ________________________________________________ _____________________________________________________________________________________

Matrix Method of Computing Area of a Polygon

Name:________________________________________ Period:___________ Date:_________________

2. Calculate the area of the pentagon with vertices (0, 2), (1, 1), (1, -2), (-2, 0) and (-3, 2).

3. Joshua has a unique fence around his house. The plans for his house are drawn on a grid. The coordinates of the corners of his fence are located at (-2, 0), (-3, -3), (1, -4) and (3, -4). Determine the area of Joshua’s land if 1 unit on the grid is 1 yard.

Name_______________________ Class Period_________ Date__________

Lesson 118 Lesson Practice

a. Calculate the determinant of [5 64 25 0

]

b. Calculate the determinant of [−2 −41 20 3

]

c. Calculate the area of the hexagon with vertices (1, 4), (2, 3), (1, -4), (-1, -4), (-2, 0) and (-1, 4)

d. The gravel for the infield of a baseball diamond forms a pentagon. The vertices of a pentagon

are located at (0, -35), (-70, 35), (-35, 70), (35, 70), and (70, 35). If one unit equals one foot,

determine the area of the field.

Geometry Lesson 118 Practice

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____ 1. Calculate the determinant of the matrix .

a. 14 c. 19

b. 29 d. 4


a. –4 c. –42

b. –2 d. –37


a. 42 c. –20

b. –23 d. 5


a. –2 c. 27

b. 26 d. 9

____ 5. The points (0, 0), and determine a triangle. Find the area of the triangle using the triangle area

formula. Then calculate the determinant of . How does the value of the determinant relate to the area

of the triangle?

a. Area = 9; The determinant is half the area of the triangle.

b. Area = 18; The determinant is the area of the triangle.

c. Area = 9; The determinant is twice the area of the triangle.

d. Area = 18; The determinant is half the area of the triangle.

____ 6. Use a determinant to calculate the area of a quadrilateral with vertices (0, 0), (3, 5), (4, 3), and (3, 1).

a. 16 square units c. 5.5 square units

b. 6.5 square units d. 8 square units

____ 7. Use a determinant to calculate the area of a quadrilateral with vertices (0, 0), (3, 5), (4, 3), and (3, 1).

a. 16 square units c. 5.5 square units

b. 6.5 square units d. 8 square units

Problem

8. Using the right triangle below, find the cosine and cotangent of angle B.

1 2 3 4 5 6–1–2 x

1

2

3

4

5

–1

–2

–3

y

A

B Ca

bc

9. The speed of a sled is measured as it slides down a steep hill. The table gives the sled’s speed at different

elapsed times.

Elapsed Time (sec) Speed (mi/h)

3 6

5 9

7 9

1 2

4 8

2 3

6 9

a. Make a scatterplot of the data in the table.

b. Use a line of best fit to estimate the speed of the sled after 4.5 seconds have elapsed.

From the book: 1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 22, 24, 25

Name:________________________________________ Period:___________ Date:_________________

Lesson 119- Platonic Solids

Regular Polyhedron (Platonic Solids)_______________________________________________________

Properties of Platonic Solids Regular Polyhedron Vertices (V) Edges (E) Faces (F) V-E+F

Tetrahedron

4 6 4

Cube

8 12 6

Octahedron

6 12 8

Dodecahedron

20 30 12

Icosahedron

12 30 20

Name:________________________________________ Period:___________ Date:_________________

1. Why are none of the platonic solids made with regular hexagons? Explain using angle measures.

2. What is the sum of the measures of the angles at a vertex of a regular octahedron?

3. What is the sum of the measures of the angles at a vertex of a cube?

4. Make a general statement about the sum of the interior angles for a vertex of a platonic solid.



a. Explain why regular octagons cannot be used to construct a Platonic solid.

b. What is the sum of the interior angles of a vertex in an icosahedon? c. Explain why four squares cannot meet at a vertex of a polyhedron.


Multiple Choice


____ 1. What is the sum of the measures of the angles at a vertex of a regular octahedron?

a. 324° d. 240° b. 300° e. 360° c. None correct

____ 2. What is the sum of the measures of the angles at a vertex of an icosahedron? a. None correct d. 240° b. 300° e. 324° c. 360°

____ 3. What is the sum of the measures of the angles at a vertex of a regular tetrahedron? a. 180° d. 360° b. 270° e. 324° c. None correct

____ 4. Identify the number of faces, edges, and vertices on the cube.

a. 8 faces, 6 edges, and 12 vertices c. 4 faces, 6 edges, and 4 vertices b. 6 faces, 8 edges, and 12 vertices d. 6 faces, 12 edges, and 8 vertices

____ 5. Identify the number of faces, edges, and vertices on the tetrahedron.

a. 4 faces, 4 edges, and 6 vertices c. 6 faces, 4 edges, and 4 vertices b. 4 faces, 4 edges, and 4 vertices d. 4 faces, 6 edges, and 4 vertices

____ 6. What is the sum of the interior angle measures at a vertex of a tetrahedron? a. 360° c. 300° b. 240° d. 180°

Problem

7. For the figure below, sketch a plane through the solid that will divide it into two congruent, reflected halves.

8. Graph the region described by the inequalities or .

9. Marcus ordered a 12-inch diameter pizza. It came cut into 12 equal slices. Since Marcus does not like pizza crust, he cuts off the end of each slice. Assume he makes a straight cut, as shown. For one slice of pizza, what is the area of the crust Marcus cuts off? Give your answer to the nearest tenth.

From the book: 1, 2, 3, 4, 5, 6, 8, 9, 11, 13, 14, 15, 16, 17, 18, 20, 21, 23, 24, 27, 29


Name:________________________________________ Period:___________ Date:_________________

Lesson 120: Topology

Topology_____________________________________________________________________________

_____________________________________________________________________________________

1. Explain why a torus, which is a doughnut shape, can be considered topologically the same as a

coffee cup.

2. Which object is topologically equivalent to the given object?

A. B. C. D.

http://datagenetics.com/blog/may32015/index.html

http://upisto.top/letter-p-

coloring-page.html

http://upisto.top/letter-c-

coloring-page.html

http://www.allkidsnetwork.

com/alphabet-stencils/

http://www.allkidsnetwork.

com/alphabet-stencils/

Name:________________________________________ Period:___________ Date:_________________

3. Classify the uppercase letters into topologically equivalent classes.

4. Sort the following symbols into topologically equivalent classes: {π,ɸ,∠,¤,Ɵ,Ψ,₀,ⱷ}



a. Is the symbol for infinity, ∞, topologically the same as the capital letter B? Explain.

b. Which object is topologically equivalent to the given object?

c. Classify the ten digits (1, 2, 3, 4, 5, 6, 7, 8, 9, 0) into topological classes by the number of

regions they divide the plane into.


Multiple Choice


____ 1. Which of the objects is topologically equivalent to this one?

a.

c.

b.

d.

____ 2. Which English letter is topologically equivalent to this Greek letter?

a.

Y

c.

A

b.

B

d.

R


a.

Q

c.

H

b.

B

d.

D


a.

O

c.

S

b.

Q

d.

B

Numeric Response

5. Find the surface area of the solid below. Round your answers to the nearest tenth of a square centimeter.

6. Find the volume, in cubic inches, of the solid shown below to the nearest tenth of a cubic inch. Assume that the prism and cylinder are right and that the top of the figure is exactly half a cylinder.

Problem

7. Classify the 14 letters shown into topologically equivalent classes.

8. Find the distance between points and . Round your answer to the nearest tenth.

8 cm8 cm

8 cm

5 cm

9 in.9 in.

9 in.

9. Find the distance between points and . Round your answer to the nearest tenth.

10. Graph the region described by the inequalities or .

From the book: 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 22, 25, 26, 27

Name:______________________________ Honors Geometry Final Study Guide 2019

Trigonometric Ratios:

sin 𝜃 =

csc 𝜃 =

cos 𝜃 =

sec 𝜃 =

tan 𝜃 =

cot 𝜃 =

Three types of transformations:

1. _______________________ 2. ______________________ 3. ______________________

Formulas:

Volume of a Sphere:

Volume of a Frustum:

Volume of a Cylinder:

Volume of a Pyramid:

Volume of a Cone:

Volume of a Cube:

Midpoint (3-D):

Distance (3-D):

Lateral Area of a Cone:

Area of a Regular Polygon:

Area of a Circle Segment:

Equation of a Circle:

Slope Formula:

Law of Cosines:

Law of Sines:


Properties:

Rhombus: Rectangle: Square:

_Ex) Equilateral_____________ __________________________ __________________________

__________________________ __________________________ __________________________

__________________________ __________________________ __________________________

__________________________ __________________________ __________________________

__________________________ __________________________ __________________________

__________________________ __________________________ __________________________

Trapezoid: Kite:

__________________________ __________________________

__________________________ __________________________

__________________________ __________________________

__________________________ __________________________

__________________________ __________________________

__________________________ __________________________

Trapezoid

Parallelogram

Rectangle Rhombus

Square

Kite

Trapezium

Quadrilateral Chart


Lesson 29 – Using the Pythagorean Theorem

1. Billy and Jane start driving from the same location. Billy dives 25 miles due north while Jane drives

35 miles due east. How far apart are Billy and Jane when they stop?

Lesson 51 – Properties of Isosceles Triangles

2. △ ABC is isosceles, and its vertex angle is at B. If 𝑚∠𝐴 = 56°, determine 𝑚∠𝐵 and 𝑚∠𝐶.

Lesson 52 – Properties of a Rhombus

3. Is the parallelogram shown a rhombus if x = 3? Show your work.

Lesson 55 – Triangle Midsegment Theorem

4. In the diagram below, 𝐹𝐺̅̅ ̅̅ is a midsegment of triangle CDE. Find the values of x and y.

9.

9.

Billy

Jane

56° C

B

A

18

2x + 6

C

D

F G

E

x

y

32

12


Lesson 64 – Angles Interior to Circles

5. Find the value of x in the diagram shown below.

Lesson 66 – Area of Regular Polygons

6. A regular hexagon has a side length of 4 ft. What is the area of the hexagon?

7. Find the area of a regular pentagon with side lengths of 19 ft and an apothem with length 13 ft.

8. Find the area of a hexagon with side lengths of 24 ft.

34°

67° x

A

B

C

D


Lesson 67 – Identifying Transformations

9. Identify the following transformations:

a.

b.

Lesson 68 – Trigonometric Ratios

10. If sin 𝜃 = .87, determine the value of cos 𝜃 to the nearest hundredth using a trigonometric ratio.

11. In the diagram below, use a trigonometric function to find a to the nearest hundredth.

12. Use the right triangle to answer parts a – b:

a. What is the sine of angle T?

b. What is the tangent of angle U?

a

4 56°

5

12

13

T

U V

A

B C

C’ B’

A’

A

B C

C’

B’

A’


13. Find x to the nearest hundredth.

14. If cos 𝜃 = .67, determine the value of sin 𝜃 to the nearest hundredth using a trigonometric ratio.

Lesson 71 – Transformations (Mapping Notation)

15. The vertices of a triangle are E(-1, -2), F(1, 2), and G(-4, 4). Find the image of △EFG after the

translation T:(x, y)→(x + 2, y + 1). Show the pre-image and image on the same coordinate grid.

Lesson 72 – Tangents and Circles

16. In ⊙S, 𝑚𝐴�̂� = 118° and 𝑚𝐶�̂� = 40°. Find 𝑚∠𝐹.

x

39°

41

Y

W

Z

B

C

A

D

F S


Lesson 73 – Angles of Elevation and Depression

17. A playground has a slide that is at a 38o angle with the ground. If the slide is 16 feet long, what is the

height?

18. A person is on the top of a 62-meter tower and sees a car below. If the angle of depression between

the top of the tower and the car below is 42°, how far, in meters, is the person from the car?

Lesson 74 – Reflections on a Coordinate Plane

19. In the diagram below, reflect △ABC across the y-axis. Find the coordinates of the vertices of the

reflected image and write the transformation in mapping notation.

Lesson 77 – Lateral Area of a Cone

20. Calculate the lateral area, in square inches, of a right cone with a radius of 3 inches and a slant height

of 9 inches to the nearest hundredth of a square inch.

A

C

B

3 in

9 in


21. Calculate the total surface area of a right cone with a radius of 2 feet and a slant height of 7 feet.

22. Calculate the volume of a right cone with a height of 10 inches and a diameter of 12 inches.

Lesson 80 – Volume of a Sphere

23. Find the volume of the sphere shown to the nearest hundredth.

Lesson 81 – Graphing a System of Linear Equations

24. Solve the system of equations graphically

𝑦 = −1

2𝑥 + 2 𝑦 =

2

3𝑥 − 5

8 in


Lesson 82 – Finding the Magnitude and Direction of a Vector

25. Add the vectors �⃑� = ⟨0, 7⟩ and �⃑⃑� = ⟨8, 0⟩, and find the magnitude and direction of the resultant

vector. Round your answers to the nearest hundredth.

Lesson 85 – Area and Perimeter of Cross Sections

26. Describe the area of the shape made by the following cross section.

Lesson 92 – Using Properties of Quadrilaterals

27. Is quadrilateral EFGH a trapezoid? Explain and show your work.

G F

E H

3


Lesson 93 – Orthographic Drawings

28. Draw the front, top, and side views of the figure. Assume there are no hidden cubes.

Lesson 94 – Law of Sines

29. Find the length, to the nearest tenth, of 𝐵𝐶̅̅ ̅̅ using the Law of Sines

Lesson 95 – Translating Circles on a Coordinate Plane

30. The equation of a circle is (𝑥 + 2)2 + (𝑦 − 1)2 = 16. What is the equation of the circle if is

translated 3 units to the right and 4 units down?

Lesson 96 – Effects of Changing Dimensions of Figures

31. One side of an equilateral triangle is dilated by a factor of 5 while the other sides remain the same.

What is the ratio of the new triangles perimeter to the original triangle’s perimeter?

A

B

C 9

52°

62°


Lesson 97 – Finding the Area of an Annulus

32. Find the area of the annulus in the concentric circles shown below. (Note: 5 cm is the radius of the

bigger circle)

33. Find the exact area (leave in terms of π) of the annulus between two concentric circles, one with a

15-inch radius and the other with a 2-inch radius.

34. This figure is made up of concentric circles on a flat surface, with dimensions as shown. If a coin is

randomly dropped onto the figure, what is the probability that it will land on the shaded region?

Lesson 98 – Law of Cosines

35. Find the length of 𝐷𝐸̅̅ ̅̅ in the triangle below. Round to the nearest hundredth.

2 cm

5 cm

D

E F 54°

13

14

12 cm

10 cm


Lesson 99 – Area and Volume Ratios of Similar Solids

36. The two cylinders shown are similar. If the volume of the smaller cylinder is 108 cubic feet, what is

the volume, in cubic feet, of the larger cylinder?

Lesson 100 – Transformation Matrices

37. Write a point matrix for 𝐸𝐹̅̅ ̅̅ . Add the point matrix to the matrix [5 5

−4 −4]. Graph the line

represented by the new matrix.

Lesson 101 – Tangents and Secants with Circles

38. In ⊙S, segment BC = 10, segment CF = 6, segment FD = 8, and segment AD = x. Find the value of

x.

1 ft

4 ft

B

C

A

D

F S

10

6

x 8

F

E


Lesson 103 – Volume of a Frustum

39. Find the volume, in cubic feet, of the frustum of the cone shown below. Round your answer to the

nearest hundredth.

40. Find the volume of this frustum of a pyramid. Round your answer to the nearest cubic meter.

41. Find the volume of this frustum of a cone to the nearest hundredth.

7.5 m

6 m

10 m

8 m

10 m

14 in.

15 in.

15 in.

3 ft

5 ft

7 ft


Lesson 104 – Relating Arc Lengths and Chords

42. Use the diagram below to prove the first part of Theorem 104-1.

Given: ⊙Q, 𝑅�̂� ≅ 𝑆�̂� Prove: 𝑅𝑆̅̅̅̅ ≅ 𝑆𝑇̅̅̅̅

Lesson 105 – Multiplying Matrices

43. Multiply the following matrices: [0 3

−4 −2] ∙ [

1 40 −3

]

Lesson 106 – Inscribed and Circumscribed Polygons

44. Find the perimeter of a regular pentagon inscribed in a circle with a radius of 8. Round your answer

to the nearest hundredth.

Statement Reasons

1. 𝑅�̂� ≅ 𝑆�̂� 1. Given

2. 2. In the same or congruent circles, congruent arcs have congruent central angles.

3. 𝑅𝑄̅̅ ̅̅ ≅ 𝑆𝑄̅̅̅̅ , 𝑇𝑄̅̅ ̅̅ ≅ 𝑆𝑄̅̅̅̅ 3.

4. 4. SAS

5. 𝑅𝑆̅̅̅̅ ≅ 𝑆𝑇̅̅̅̅ 5.

Q

R

S

T

8 in

8 in


45. Find the perimeter of a regular octagon that is inscribed in a circle with a radius of 6. Round your

answer to the nearest tenth.

46. Find the perimeter of an equilateral triangle inscribed in a circle with a radius of 7. Round your

answer to the nearest whole number.

47. Find the area of a circumscribed square if the inscribed circle has a diameter of 5 centimeters.

Lesson 110 – Golden Ratio

48. If a and b are in the golden ratio and a is the larger number. Find the value of b if a = √5.


Lesson 111 – Distance and Midpoint in 3-D

49. Find the distance between the following 2 points X( 1, -2, 5) and Y(-6, 4, 3) to the nearest tenth.

50. Find the distance between R(0, 12, -2) and S(6, 8, -3).

51. Find the midpoint of F(22, 14, 9) and G(15, -8, -6).

52. The endpoints of 𝑆𝑇̅̅̅̅ are S(-11, 10, 13) and T(14, 11, 6). What is the midpoint of 𝑆𝑇̅̅̅̅ ?

Lesson 112 – Area of a Sector

53. Determine the area, in square inches, of the shaded segment of ⊙A in the diagram below. Round

your answer to the nearest hundredth.

8

4 in

A


54. A circle has a radius of 5 inches. Determine the area of the segment formed by a chord with

a central angle of 36o. Round your answer to the nearest tenth of a square inch.

Lesson 114 – Graphing Systems of Linear Inequalities

55. Graph 𝑥 − 4𝑦 < 7𝑥 + 8

56. Graph the following system of inequalities:

𝑦 ≤ −1

2𝑥 + 3 𝑎𝑛𝑑 𝑦 >

4

3𝑥 + 2


Lesson 115 – Surface Area and Volume of Composite Solids

57. Find the volume of the solid shown below to the nearest tenth. Assume that the prism and cylinder are right and that the top figure is exactly half of a cylinder.

Lesson 116 – Cosecant, Secant, and Cotangent Ratios

58. Find the value of the cosecant, secant, and cotangent of θ in a triangle.

59. Write expressions for the values of sin Q, cos Q, tan Q, secant Q, cosecant Q, and cotangent Q in

this figure.

4 in

4 in

4 in

θ

8

24

18

θ

x

z

y Q


Lesson 117 – Lines of Best Fit and Correlation

60. Determine the type of correlation shown in the scatterplot below.

Lesson 118 – Finding the Determinant and the Area of a Polygon Using the Determinant

61. Find the determinant of the following matrix.

62. Find the area of a polygon with the vertices (3, 6), (4, 1), (-1, 1), (2, -1) and (3, -2).

[6 5

−4 4−2 −1

]


63. Calculate the determinant of [−2 −41 20 3

]

64. Calculate the area of the hexagon with vertices (1,4), (2,3), (1,-4), (-1,-4), (-2,0), and (-1,4).

Documents

Geometry Week of June 8th - June 15th Grades 9 and 10_Geom_Week_June… · Geometry Week of June 8th - June 15th S u b mi s s i on : P l e a s e s ubm i t a l l of *your a s s i gnm