Geometry Unit 7 Note Sheets

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Date Name of Lesson

8.2 The Pythagorean Theorem and its Converse

8.3 Exploring Special Right Triangles (45-45-90) Used with Special Rt Tri Pt 1

8.3 Special Right Triangles Part 1

8.3 Exploring Special Right Triangles (30-60-90) Used with Special Rt Tri Pt 2

8.3 Special Right Triangles Part 2

8.3 Worksheet Review of Special Right Triangles

Quiz 8.2-8.3

8.4 Trigonometry Part 1

8.4 Trigonometry Part 2

8.4 Rearranging SOHCAHTOA Activity

Quiz 8.4

8.5 Angles of Elevation and Depression

8.5 Shadow Activity with Worksheet

Practice Test

Unit Test

Geometry Unit 7 Note Sheets

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8.2 The Pythagorean Theorem and Its Converse Notes Sheet

Pythagorean Theorem

Guided Practice

Find x.

1. 2.

Your Turn

3. 4.

Pythagorean Triples

Geometry Unit 7 Note Sheets

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Guided Practice

Use a Pythagorean Triple to find x. Explain your reasoning.

5. 6.

Your Turn

7. 8.

Converse of the Pythagorean Theorem

Pythagorean Inequality to Prove Acute Triangles

Pythagorean Inequality to Prove Obtuse Triangles

Guided Practice

Determine whether each set of numbers can be the measures of a triangle. If to, classify the triangle as acute,

right or obtuse. Justify your answer.

9. 7, 14, 16 10. 6.2, 13.8, 20

Your Turn

11. 9, 12, 15 12. 10, 11, 13

Geometry Unit 7 Note Sheets

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8.3 Exploring Special Right Triangles (45-45-90) Given the isosceles right triangle to the right…

1. What is the measure of each angle? Explain

2a. If the length of each leg is 1 unit, find the length of the hypotenuse. Leave your answer in simplified

rational form.

2b. What are the side-length ratios of leg : leg : hypotenuse?

3. If the length of each leg is 2 unit, find the length of the hypotenuse. Leave your answer in simplified rational

form.

Geometry Unit 7 Note Sheets

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8.3 Special Right Triangles Part 1 Notes Sheet

45° − 45° − 90° Triangle Theorem

Guided Practice

Find x.

1. 2.

Your Turn

3. 4.

Guided Practice

5. 6.

Geometry Unit 7 Note Sheets

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Your Turn

7. 8.

Guided Practice

Find x and y.

9.

Your Turn

10.

Geometry Unit 7 Note Sheets

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8.3 Exploring Special Right Triangles (30-60-90) Given the equilateral triangle to the right whose sides are 2 units long…

1. What is the measure of each acute angle?

2. Fold the triangle along vertex A so that vertex B maps onto vertex C. Draw a segment along the crease.

Label point D where the new segment intersects BC. What is special about AD? What is the length of BD

(label it in the diagram)? Explain your reasoning.

3. What does AD do to angle A?

4. Examine triangle ABD. What is the measure of angle BAD and BDA (Label it in the diagram above)?

5. Find the length of AD. Leave your answer in simplified radical notation.

Geometry Unit 7 Note Sheets

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8.3 Special Right Triangles Part 2 Notes Sheet

30° − 60° − 90° Triangle Theorem

Guided Practice

Find x and y.

1. 2.

3.

Geometry Unit 7 Note Sheets

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Your Turn

4. 5.

Guided Practice Your Turn

Find x and y. 7.

6.

Guided Practice

6.

Geometry Unit 7 Note Sheets

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8.4 Trigonometry Part 1 Notes Sheet

Words Symbols

Sine

Cosine

Tangent

Guided Practice

Express each ratio as a fraction and as a decimal to the nearest hundredth.

1. 𝐬𝐢𝐧𝑷

2. 𝐬𝐢𝐧𝑸

3. 𝐜𝐨𝐬𝑷

4. 𝐜𝐨𝐬𝑸

5. 𝐭𝐚𝐧𝑷

6. 𝐭𝐚𝐧𝑸

Your Turn

7. 𝐬𝐢𝐧𝑲

8. 𝐜𝐨𝐬𝑲

9. 𝐭𝐚𝐧𝑲

10. 𝐬𝐢𝐧 𝑱

11. 𝐜𝐨𝐬 𝑱

12. 𝐭𝐚𝐧 𝑱

Geometry Unit 7 Note Sheets

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Guided Practice

Find x to the nearest hundredth.

13. 14.

Your Turn

15. 16.

Guided Practice

17. Use a special right triangle to express the tangent of 30° as a fraction and as a decimal to the nearest

hundredth.

Your Turn

18. Use a special right triangle to express the cosine of 45° as a fraction and as a decimal to the nearest

hundredth.

Guided Practice

19. A certain part of a hiking trail slopes upward at about a 5° angle. After traveling a horizontal distance of

100 feet along this part of the trial, what would be the change in the hiker’s vertical position? What distance

has the hiker traveled along the path?

Your Turn

20. A fitness trainer sets the incline on a treadmill to 7°. The walking surface is 5 feet long. Approximately

how many inches did the trainer raise the end of the treadmill from the floor?

Geometry Unit 7 Note Sheets

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8.4 Trigonometry Part 2 Notes Sheet

Inverse Trigonometric Ratios

Inverse Sine

Inverse Cosine

Inverse Tangent

Guided Practice

Use a calculator to find the measure of ∠𝐴 to the nearest tenth.

1. 2.

Your Turn

3. 4.

Geometry Unit 7 Note Sheets

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Guided Practice

5. Solve the right triangle. Round side measures to the nearest tenth and angle measures to the nearest degree.

𝑚∠𝑋

𝑚∠𝑌

𝑋𝑌

Your Turn

Solve the right triangle. Round side measures to the nearest tenth and angle measures to the nearest degree.

6.

7.

Geometry Unit 7 Note Sheets

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8.5 Angles of Elevation and Depression Notes Sheet

Vocabulary:

Angle of elevation __________________________________________________________________________

__________________________________________________________________________________________

Angle of depression _________________________________________________________________________

__________________________________________________________________________________________

Guided Practice

Name the angle of depression or angle of elevation in each figure.

1. 2.

Your Turn

3. 4.

Guided Practice

5. Jay is meeting friends at the castle in the center of an amusement park. He sights the top of the castle at an

angle of elevation of 38°. From the park’s brochure, she knows that the castle is 190 feet tall. If Jay is 5.5 feet

tall, about how far is he from the castle to the nearest foot?

Your Turn

6. The cross bar of a goalpost is 10 feet tall. If a field goal attempt is made 25 yards from the base of the

goalpost that clears the goal by 1 foot, what is the smallest angle of elevation at which the ball could have been

kicked to the nearest degree? (hint is everything in the same units of measure?)

Geometry Unit 7 Note Sheets

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Guided Practice

7. A search and rescue team is airlifting people from the scene of a boating accident when they observe another

person in need of help. If the angle of depression to this other person is 42° and the helicopter is 18 feet above

the water, what is the horizontal distance from the rescuer to this person to the nearest foot?

Your Turn

8. A lifeguard is watching a beach from a line of sight of 6 feet above the ground. She sees a swimmer at an

angle of depression of 8°. How far from the tower is the swimmer?

Guided Practice

9. Mia is at the top of a cliff and sees a seal in the water. If the cliff is 40 feet above the water and the angle of

depression is 52°, what is the horizontal distance from the seal to the cliff, to the nearest foot?

Your Turn

10. A hockey player takes a shot at a distance of 20 feet away from a 5-foot goal. If the puck travels at a 15° angle of elevation towards the center of the goal, will the player score?