high school geometry yearlong

High School Geometry Yearlong

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Embedded Assessment 1Use after Activity 10

TransformationsDESIGNING THE PLAZA

City planner Regina Kane is designing a new plaza for the city. Her plan is organized on a coordinate plane, as shown and described below.

4

6

8

10

2

–2

–4

–6

–8

–10

2–2–4–6–8–10 4 6 8 10

y

x

T

Hexagonal fountain: centered at (0, 0), two sides of length 2 unitsShort rectangular benches: centered at (0, 10) and (0, −10), length 4 unitsLong rectangular benches: centered at (10, 0) and (−10, 0), length 8 unitsTriangular statue T: vertices at (5, 10), (7, 10), (7, 7)Flagpoles (shown as dots): at (−2, 10) and (2, −10), next to short benches

1. Why could a single translation map one of the long rectangular benchesonto the other long rectangular bench, but not map one shortrectangular bench and flagpole onto the other short rectangular benchand flagpole?

2. Describe a rigid motion or composition of rigid motions that maps therectangular bench at (0, 10) and the adjacent flagpole onto the othershort rectangular bench and flagpole.

3. Regina wants to know if it is possible for a composition of rigid motionsto map one of the short rectangular benches onto a long rectangularbench. Write a short explanation that you could send to Regina in anemail.

4. One of Regina’s assistants glances at the plan and comments that thehexagonal shape has the greatest number of lines of symmetry of all theshapes in the plan. Is the assistant correct? Explain.

5. A landscape architect recommends installing a triangular statue withvertices at (10, −10), (10, −8), and (7, −10). a. Is the triangle congruent to triangle T ? Justify your answer. b. Propose a series of rigid motions that justifies your answer to part a.

6. Another landscape architect recommends installing a triangular statuewith vertices at (−5, 10), (−5, 8), and (−7, 8). a. Is the triangle congruent to triangle T ? Justify your answer. b. Propose a series of rigid motions that justifies your answer to part a.

Unit 2 • Transformations, Triangles, and Quadrilaterals 141

Geometry Yearlong 1

Transformations 1. 2.

3. 4.

Geometry Yearlong 2

Transformations 5. 6.

7.

Geometry Yearlong

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Similarity 1. 2.

3. 4.

Geometry Yearlong 4

Similarity 5.

Geometry Yearlong

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QuadrilateralsLUCY LATIMER’S LOGO

Lucy Latimer acquired a new company in a hostile takeover. This new company, Math Manipulatives, needed a new logo. Ms. Latimer’s husband teaches geometry, and his class submitted a logo and the following instructions for reproducing the logo.• Begin with a large isosceles trapezoid, and locate the midpoint of

each side.• Use these midpoints as the vertices of a new quadrilateral to be formed

inside the first quadrilateral.• Locate the midpoint of each side of the second quadrilateral, and use

these midpoints as vertices to form a third quadrilateral.• Repeat this process with each new quadrilateral until the newest

quadrilateral is too small to be seen.

Suppose you were one of Ms. Latimer’s employees, and she assigned you the task of investigating this design proposal. Write a report to be sent to Ms. Latimer. In your report, you should include:

1. a reproduction of this design on a piece of graph paper. (You must showat least six quadrilaterals, including the first.)

2. how you know that your first quadrilateral is an isosceles trapezoid.3. the best name (trapezoid, parallelogram, rectangle, rhombus, or square)

for each subsequent quadrilateral and a convincing argument thatsupports the name you chose.

4. a description of any patterns that you may find in the sequence of theshapes.

5. definitions, postulates, and theorems from geometry to support yourclaims.

Unit 2 • Transformations, Triangles, and Quadrilaterals 237

Geometry Yearlong 6

Triangles & Quadrilaterals 1. 2.

3. 4.

Geometry Yearlong 7

Triangles & Quadrilaterals 5.

Geometry Yearlong

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Right TrianglesPOWERED BY THE WIND


Yoshio owns a farm that uses wind turbines to produce wind power. Wind power, also known as wind energy, uses the power of the wind to generate electrical or mechanical power.

1. One of the wind turbines that Yoshio owns is shown in the figure below.He needs to know the height of the turbine. Yoshio is 5 feet 6 inches tall.If he stands 12 feet from the turbine, his line of sight forms a 90° anglewith the top and bottom of the turbine.

a. What special segment is ZW? Explain. b. Write a similarity statement to show the relationship among

triangle XYZ and the two triangles formed by drawing ZW. c. What is the height of the turbine?

2. Another wind turbine that Yoshio owns uses guy wires for support.In the figure, AC = 15 ft, m ABC∠ = 60o, m ADC∠ = 45o, andm AEC∠ = 30o.

Find each of the following measures. a. AB = b. AD = c. AE = d. What is the height of the turbine, EC?

3. Use the converse of the Pythagorean Theorem to prove that triangleAEC is a right triangle.

12 ft

5.5 ft

X

Y

WZ

A C

E

D

B

Unit 3 • Similarity and Trigonometry 301

Geometry Yearlong 9

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TrigonometryZIPPING ALONG


Chloe wants to ride a zip line. She looked online and found a zip line tour near her home, and she needs to decide whether to ride the Beginner’s zip line or the Daredevil’s zip line. The tour company’s Web page gives some of the measurements for the two zip lines, but Chloe wants to find some additional measurements before she decides. The image below is shown on the tour company’s Web page.

1. Chloe printed the image and added labels to help her identify sides andangles. Describe how to find BC, the difference in the heights of thestarting points.

2. Find each of the following measures. Round your answer to the nearestwhole number or degree. a. BC = b. m B∠ = c. m BCA∠ = d. m CAD∠ = e. m DCA∠ = f. AD =

3. What is the height of the starting point of the Beginner’s zip line, CD?4. What is the height of the starting point of the Daredevil’s zip line, BD?

To prepare for her zip line adventure, Chloe’s father helps her build a smaller zip line in her backyard. Chloe made a diagram of her zip line.

wire for zip line

Starting point, S

E B

5. The height of the starting point, SB, is 20 feet and EB = 26 feet. Determinethe angle of elevation from the ending platform, E, to the starting point, S.Show the work that leads to your response. Round your angle to thenearest degree.

20°

420 ft

500 ft

Daredevil’s zip line

Beginner’s zip line

20°

420 ft

500 ft

Daredevil’s zip line

Beginner’s zip line

A D

C

B

Unit 3 • Similarity and Trigonometry 331

Geometry Yearlong 10

Pythagorean & Trigonometry 1. 2.

3. 4.


Pythagorean & Trigonometry 5. 6.

7. 8.

Geometry Yearlong

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PyramidsThree of the great Egyptian pyramids are pictured below. Each is a square pyramid.

1. 1. Calculate the missing information for each the 3 individual pyramids based on the given measurements:

i. The great Pyramid of Menkaure has a height of about 215 feet and a base side length of about 339 feet. What is

its volume?

ii. The great Pyramid of Khafre has a volume of about 74,400,000 cubic feet and a base side length of 706 feet.

What is its height?

iii. The great Pyramid of Khufu has a volume of about 86,700,000 cubic feet and a height of 455 feet. What is the

length of its base?

2. The Great Pyramid of Khufu once stood 26 feet taller than it is today. Calculate the original volume of the

Great Pyramid. Similarly, the Pyramid of Khafre has eroded over time and lost some of its height. If the

original volume of the pyramid was approximately 78,300,000 cubic feet, what was its original height?


high school geometry yearlong

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