Geometry Week of May 11th - May 15th › Math - Geometry - Week of May...Geometry Lesson 107 Practice Mrs. Rogers Multiple Choice Identify the choice that best completes the statement

Geometry Week of May 11th - May 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. IXL: All students should have the IXL username and password but if there are any problems logging in please contact your teacher as soon as possible. Please make sure that you are completing the assigned section letter and number for each lesson . This is acting as your lesson practice for each of these lesson topics so I am expecting to see roughly a half hour of time spent on the IXL topic each day. Homework: The lessons homework is also expected to be completed within two days of the video lesson (example: Monday’s hw will be due on Wednesday, Thursday and Fridays HW will be due on Monday). You will be responsible for completing the homework assignment for that lesson and submitting it via email. The lesson Practice will be due the day after the assigned video lesson (example: Tuesday’s Lesson Practice will be due Wednesday) 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. The points awarded to each assignment is indicated below. Note: Attached at the end is study guide 20. This study guide will be due before the accuracy assessment for next week and will not be due this week. Assignments: Monday: Study Guide 19 is due today (10 points) Submit by 11:59 on Monday 5/11 by 11:59 pm Tuesday: Complete Accuracy assignment on Microsoft teams. The assignment is based off of study guide 19 (48 points) Submit by 11:59 on Thursday 5/14 Wednesday: Watch video on Lesson 107 and Lesson Practice 107 (10 points) and Lesson 107 HW *CP complete attached worksheet, Honors, Complete book problems 1-30* (10 points) Submit by 11:59 on Friday 5/15 Thursday: Watch video on Lesson 108 and Lesson practice 108 (10 points) and Lesson 108 HW *CP complete attached worksheet, Honors, Complete book problems 1-30* (10 points) Submit by 11:59 on Monday 5/18 Friday: Watch video on Lesson 109 and Lesson Practice 109 (10 points) and Lesson 109 HW *CP complete attached worksheet; Honors, complete book problems 1-30* (10 points) submit by 11:59pm on Monday 5/18. 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 107 – Maximizing Area

1. Rectangle QRST’s base is b, its height is h, and it has a perimeter of 24 units. a. Determine the area of the rectangle for b = 2, b = 4, b = 6, b = 8.

b. Based on the results of part a, what conjecture can you make about maximizing the area of a rectangle with a fixed perimeter?

Name:________________________________________ Period:___________ Date:_________________

2. The perimeter of each figure below is 30 units. Find and compare their areas. Then make a

conjecture about the relationship between the number of sides of a polygon and its area for a fixed perimeter.

Result

5ξ3

10 7.5

4. 13

6

5ξ3

2

5

Name_______________________ Class Period_________ Date__________

Lesson 107 Lesson Practice a. A rectangle has a perimeter of 144 inches. Determine the area of the rectangle for b = 9 inches, b = 12 inches and b = 18 inches. b. What is the maximum area of a rectangle with a perimeter of 144 inches?

c. Explain which of these two triangles has the greater area: A triangle with side lengths of 20, 20 and 2, or a triangle with side lengths of 6, 8, and 8? d. A rectangular patio is to be made from 625 square tiles. The tiles will be placed so that the patio will have the least possible perimeter. How many tiles will be placed along the length of the width of the patio?

Name:__________________________________________ Period:_____________ Date:_____________

Geometry Lesson 107 Practice

Mrs. Rogers

Multiple Choice

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

____ 1. Compare the area and circumference of a circle with a radius of 15 cm with the area and perimeter of a square

that has sides measuring 26.59 cm.

a. The circle and the square have approximately the same area, but the circumference of the

circle is greater than the perimeter of the square.

b. The area of the square is greater than the area of the circle, but the circumference of the


c. The circle and the square have approximately the same area and the circumference of the

circle is approximately equal to the perimeter of the square.

d. The circle and the square have approximately the same area, but the perimeter of the

square is greater than the circumference of the circle.

____ 2. Compare the area and circumference of a circle with a radius of 12 ft with the area and perimeter of a square

that has sides measuring 21.27 ft.

a. The circle and the square have approximately the same area, but the circumference of the


b. The circle and the square have approximately the same area, but the perimeter of the


c. The area of the square is greater than the area of the circle, but the circumference of the


d. The circle and the square have approximately the same area and the circumference of the


____ 3. Compare the area and circumference of a circle with a radius of 19 ft with the area and perimeter of a square

that has sides measuring 33.68 ft.

a. The area of the square is greater than the area of the circle, but the circumference of the


b. The circle and the square have approximately the same area, but the perimeter of the


c. The circle and the square have approximately the same area, but the circumference of the


d. The circle and the square have approximately the same area and the circumference of the


____ 4. Volunteers at an animal rescue shelter are building a new play yard for dogs. They have 194 meters of fencing

available. What is the maximum area they can enclose?

a. 2352.25 m? c. 9409 m?

b. 3528.38 m? d. 2090.89 m?



a. 8464 m? c. 2750.8 m?

b. 1880.89 m? d. 2116 m?

Name:__________________________________________ Period:_____________ Date:_____________



a. 8464 m? c. 2327.6 m?

b. 2116 m? d. 1880.89 m?



a. 3364 m? c. 747.56 m?

b. 925.1 m? d. 841 m?

Numeric Response

8. Alan is installing a patio that will contain 729 stone tiles. Each tile measures foot by foot. Alan does not

know the exact dimensions of the finished patio, but he knows that it is rectangular. What is the minimum

perimeter, in feet, the finished patio could have?







Name:__________________________________________ Period:_____________ Date:_____________

Problem

11. Rectangle EFGH’s base is b, its height is h, and it has a perimeter of 48 units. Determine the area of the

rectangle for , , , and . Based on these results, what conjecture can you make about

maximizing the area of a rectangle with a fixed perimeter?










Name:__________________________________________ Period:_____________ Date:_____________

15. A square and a regular hexagon are inscribed in congruent circles.

Figure 1 Figure 2

a. For Figure 1, find the percent of the area of the circle that is inside the square. Use 3.14 for , and round

your answer to the nearest tenth of a percent.

b. For Figure 2, find the percent of the area of the circle that is inside the regular hexagon. Use 3.14 for , and

round your answer to the nearest tenth of a percent.

c. Compare the ratios.

d. Predict the percent of the area of a circle that would be inside an inscribed regular octagon.

Name:__________________________________________ Period:_____________ Date:_____________

Name:________________________________________ Period:___________ Date:_________________

Lesson 108 – Introducing to Coordinate Space

Z-Axis________________________________________________________________________________

Three- Dimensional Coordinate System_____________________________________________________

Ordered Triples________________________________________________________________________

_____________________________________________________________________________________

1. In the given cube, identify the coordinates of the vertices.

2. Plot the point A(3, 1, 5) on a three-dimensional system..

http://mathsfirst.massey.ac.nz/Algebra/CoordSystems/Coordinates3D.htm

Name:________________________________________ Period:___________ Date:_________________

3. Determine the coordinates of two points that are collinear with the points R(3, 5, 7) and S(4, 6, 12).

4. In a three-dimensional space, two electrons start from a point located at (5, -1, 4). One electron moves to the point (9, -4, 6) while the other moves to the point (13, -7, 8). Are the two electrons moving in a collinear path? Explain.


Lesson 108 Lesson Practice

a. Identify the coordinates of the vertices of this rectangular prism.

b. Plot the point J (3, -1, 2) on a three-dimensional coordinate system.

c. Determine the coordinates of two points that are collinear with the line through the points

A(2, -2, 3) and B(1, -5, 5).

d. A charged particle is moving along a line. First it passes through the point (4, 7, 2) and then

through (1, 12, 13). Will the particle hit a target located at (-11, 32, 60)? Explain.

Name:__________________________________ Period:__________ Date:________________


Mrs. Rogers

Multiple Choice


____ 1. Find the perimeter of a circumscribed regular hexagon if the inscribed circle has a radius of 20 units. Round

to the nearest tenth.

a. 138.6 d. 115.5

b. 69.3 e. None correct

c. 23.1

____ 2. Give the coordinates of the image of the triangle after a dilation centered at the origin and with a scale factor

of 0.1.

a. F´(0.6, 0.5), G´(1, 0.1), H´(0.2, 0.1)

b. F´(0.5, 0.6), G´(0.1, 1), H´(0.1, 0.2)

c. F´(0.6, 0.5), G´(1, 0.1), H´(2, 1)

d. F´(–0.6, –0.5), G´(–1, –0.1), H´(–0.2, –0.1)

____ 3. Find the volume of the frustum of the cone. Use 3.14 for . Round your answer to the nearest tenth.

a. 69.6 in3 c. 60.0 in3

b. 68.7 in3 d. 47.6 in3

F

GH

1 2 3 4 5 6 7 8 9 10 11 12 x

1

2

3

4

5

6

7

8y

Name:__________________________________ Period:__________ Date:________________

____ 4. . AB = 2x + 5, and CD = 7x – 10. Find AB and CD.

a. AB = 11; CD = 11 c. AB = 3; CD = 3

b. AB = 35; CD = 35 d. AB = 7; CD = 7

____ 5. Tell whether the product of is defined. If so, give the dimensions of PQ.

a. defined; c. defined;

b. defined; d. undefined

____ 6. Find the product AB, if possible.

A = B =

a.

c.

b.

d. Not possible

____ 7. The regular hexagon is inscribed in the larger circle and circumscribed about the smaller circle. Find the area

of the smaller circle if the radius of the larger circle is 17 units. Use 3.14 for , and round your answer to the

nearest hundredth.

a. 907.46 units? c. 680.6 units?

b. 226.87 units? d. 952.84 units?

A

B

C

D

17

Name:__________________________________ Period:__________ Date:________________

____ 8. Identify the coordinates of point B.

a. (0, –5, 3.5)

c. (–5, 0, 3.5)

b. (0, 3.5, 3.5)

d. (–5, 3.5, 0)

____ 9. Graph (–2, 3, 1) on a three-dimensional coordinate system.

a.

c.

b.

d.

Name:__________________________________ Period:__________ Date:________________

____ 10. Which point is collinear with (2, 5, 3) and (5, 1, 6)?

a. (8, 5, 9) c. (8, –3, 8)

b. (–1, 9, 0) d. (4, 3, 5)

Numeric Response

11. Find the perimeter of a regular pentagon that is inscribed in a circle with a radius of 4. Round your answer to

the nearest hundredth.

Problem

12. Determine the result of the dilation on the points (2, 3) and (–4, –3).

13. The cube shown below has a side length of 3 units and vertex A at A (0, 0, 0). Identify the coordinates of the

other vertices.

x

EH

D

CB

F

G

A1 2 3 4 5–1–2–3–4–5–6 y

1

2

3

4

5

6

–1

–2

–3

–4

–5

–6

z

Name:__________________________________ Period:__________ Date:________________

14. Determine the coordinates of two points that are collinear with the points and .

Name:__________________________________ Period:__________ Date:________________

Name:________________________________________ Period:___________ Date:_________________

Lesson 109 – Non-Euclidean Geometry

Euclidean geometry_____________________________________________________________________

_____________________________________________________________________________________

Non-Euclidean Geometry________________________________________________________________

Spherical Geometry_____________________________________________________________________

1. Identify a great circle, a segment, an angle, and a triangle on the sphere.

2. Classify the triangle shown according to its angle measures and side lengths.

A

C D

B

B

A

C

Name:________________________________________ Period:___________ Date:_________________

Area of a Spherical Triangle

3. Find the area of the spherical triangle when the radius of the sphere is 3 meters. Round your

answer to the nearest hundredth.

C

A

B

80°

85°

85°


Lesson 109 Lesson Practice a. Identify a great circle, a segment, and a triangle on the sphere. b. Classify the triangle as equilateral, isosceles, or scalene

c. Find the area of the spherical triangle to the nearest tenth. The diameter of the sphere is 24 inches.

Name:________________________________________ Period:_________ Date:________________


Mrs. Rogers

Multiple Choice


____ 1. Name a great circle, a segment, and a triangle on the sphere.

a. great circle BC, c. great circle AB,

b. great circle AD, d. great circle BC,

____ 2. Classify as equilateral, isosceles, or scalene.

a. equilateral b. isosceles c. scalene

B

A

C

DF

E

B

A

C

DF

G

Name:________________________________________ Period:_________ Date:________________

____ 3. Find the area of spherical on a sphere with radius 8 cm, given that

. Round to the nearest tenth.

a. c. b. d.

____ 4. Find if . Round your answer to the nearest hundredth.

a. c. b. d.

____ 5. A line segment is translated 2 units left and 4 units up. Which is the transformation matrix?

a.

d.

b.

e. None correct

c.

____ 6. Find AB. Round your answer to the nearest tenth.

a. AB = 13.8 c. AB = 33.8

b. AB = 10.4 d. AB = 14.5

____ 7. Find AC. Round your answer to the nearest tenth.

a. AC = 17.5 c. AC = 16.6

b. AC = 306.1 d. AC = 10.3

A

B

C

50°

62°

12

A

B

C

105°10

12

Name:________________________________________ Period:_________ Date:________________

____ 8. Add the two matrices, if possible.

+ .

a.

c.

b. Not possible d.

Problem

9. In the diagram below, identify a great circle, a segment on the sphere, an angle, and a triangle.

10. Classify triangle DEF shown below according to its angle measures and side lengths.

11. The diagram below shows the first two iterations of a fractional pattern. Draw the third iteration.

Name:________________________________________ Period:_________ Date:________________

Student Name (Please Print):_______________________________________________________

Mystic Valley Regional Charter School

Test Study Guide

Be able to define, understand, and use the following properties, terms, and concepts:

• Surface Area of a Sphere

• Solution to a Systems of equations

• How to find Magnitude and Direction of a vector

• Trig functions (SOH-CAH-TOA)

• Inverse Trig Functions

• Perimeter and Area ratios

• Law of Sines

• Adding Matrices

• Orthographic drawings

• Concentric Circles

• Equations of circles

• Law of Cosines

Refer to the following Homework Problems and Lesson Practice Problems for practice.

Remember to use your corrected homework and practice to check your work. You must try

the indicated problem. If you have difficulty with a problem type, do more practice

problems!

Course: Geometry Test Number: 20 Lessons Covered: 1 INV 10 Test Date: Friday, May 7, 2019

Lesson Taught

Problem Type Lesson Practice Examples

Homework Examples

79 Angles Exterior to Circles 79 c, d HW L79 #8, 21

HW L79 #21

80 Surface area of a Sphere 80 a HW L80 #2

80 a

81 Determining if a System of Equations has a solution 81 d Example 3 from page 533 is a good

example to look at also

Pg 533 Example 3

82 Inverse Trig Functions 82 a, b HW L82 #1

HW L82 #1

83 Add Vectors to Find Magnitude and Direction of Resultant Vector

83 c Example 3 on page 544 is a good


83 c

84 Dilations 84 d HW L84 #19

Example 4 on page 549 is a good


HW L84 #19

86 Determining Chord Length 86 a HW L86 #1

86 a

87 Area ratios of similar figures 87 d HW L87 #1, 10, 24

87 d

88 Solve Inequalities 88 a HW L88 #3

88 a

91 Applying Trig Identities to Distance Problems 91 c Example 3 on page 596 is a good


91 c

92 Quadrilaterals on a Coordinate Plane 92 b, d HW L92 #10

92 b, d

93 Orthographic Drawings 93 a-c HW L93 #28

93 a

94 Law of Sines 94 b HW L95 #15 Example 2 from page

614 is a good example to look at

also

94 b

95 Determining Equations of Dilated Circles 95 b, c HW L95 #24

95 b, c

96 Effects of changing dimensions on Perimeter and Area

96 a Example 1 from page 624 is a good


96 a

97 Determine of Circles are Concentric or not 97 a

97 a

98 Law of Cosines 98 a HW L98 #1, 11 HW L99 #1

98 a

99 Perimeter Ratios of 3-D Solids 99 a HW L99 #5

99 a

100 Adding Matrices 100 a-b

100 a

Inv 10 Fractal Patterns Inv 10 a.

Inv 10 a.

Documents

Geometry Week of May 11th - May 15th › Math - Geometry - Week of May...Geometry Lesson 107 Practice Mrs. Rogers Multiple Choice Identify the choice that best completes the statement