Geometry Chapter 7 Capacity Matrix

Right Triangles and Trigonometry

Learning Targets: The student can:

find the geometric mean of right triangles. use the special right triangles to find the lengths of sides. use SohCahToa to find lengths of sides and angles in right triangles. use the Law of Sines to find the lengths of sides and angles in any triangle. use the Law of Cosines to find the lengths of sides and angles in any triangle.

Section Required Assignments Additional Resources Sec 7-1

Geometric Mean (Formative

Assessments)

⎕ Chapter 7 Triple Entry Journal

⎕ Sec 7-1 #’s 13, 15, 17, 19, 21, 25, 27, 29, 31 (9 questions)

⎕ Sec 7-1 #’s 1-12

⎕ Pg 766 Lesson 7-1 #’s 1-12

Sec 7-2 The Pythagorean Theorem and Its

Converse (Formative

Assessments)

⎕ Sec 7-2 #’s 13, 15, 17, 19, 21, 23, 25, 41 (8 questions)

⎕ Q1 Pythagorean Theorem (iXL)

⎕ Q2 Converse of the Pythagorean Theorems (iXL)

⎕ Sec 7-2 #’s 1-11 ⎕ Pg 767 Lesson 7-2 #’s 1-13

Sec 7-3 Special Right

Triangles (Formative

Assessments)

⎕ Sec 7-3 #’s 13, 15, 17, 19, 21, 23, 25, 27, 29, 37 (10 questions)

⎕ Q4 Special right triangles (iXL)

⎕ Sec 7-3 #’s 1-11 ⎕ Pg 767 Lesson 7-3 #’s 1-6

Quiz on Sec 7-1 to 7-3

Summative Assessment

Must score > 70

Things you should know:

Do you know the geometric mean formula? (Sec 7-1)

Do you know that when you draw an altitude in a right triangle from the right angle to the hypotenuse, it creates 2 smaller triangles that are similar to the large triangle? (Sec 7-1)

Can you set up proportions using the situation above? (Sec 7-1)

Do you know Pythagorean Theorem? (Sec 7-2)

What does the Pythagorean Theorem help us find? (Sec 7-2)

What does the Converse of the Pythagorean Theorem tell us? (Sec 7-2)

Do you know your two special right triangles? (Sec 7-3)

Sec 7-4 Trigonometry

(Formative Assessments)

⎕ Sec 7-4 #’s 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 53 (17 questions)

⎕ R1 Trigonometric ratios: sin, cos, and

⎕ Sec 7-4 #’s 1-17 ⎕ Pg 767 Lesson 7-4 #’s 1-13

tan (iXL)

⎕ R7 Inverses of trigonometric functions (iXL)

Sec 7-5 Angle of

Elevation and Depression

(Formative Assessments)

⎕ Sec 7-5 #’s 9, 11, 13, 14, 15, 21, 22, 23 (8 questions)

⎕ Sec 7-5 #’s 1-7 ⎕ Pg 768 Lesson 7-5 #’s 1-3

Sec 7-6 The Law of Sines

(Formative Assessments)

⎕ Sec 7-6 #’s 17, 19, 21, 23, 25, 27, 29, 33, 35, 38, 39 (11 questions)

⎕ R11 Law of Sines (iXL)

⎕ Sec 7-6 #’s 1-15

⎕ Pg 768 Lesson 7-6 #’s 1-8

Sec 7-7 The Law of

Cosines (Formative

Assessments)

⎕ Sec 7-7 #’s 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33 (12 questions)

⎕ R12 Law of Cosines (iXL) ⎕ R13 Solve a triangle (iXL)

⎕ Sec 7-7 #’s 1-10 ⎕ Pg 768 Lesson 7-7 #’s 1-7

Quiz on Sec 7-4 to 7-7

Summative Assessment

Must score > 70

Things you should know:

Do you know what SohCahToa means? (Sec 7-4)

Do you know what SohCahToa helps you find? (Sec 7-4)

Can you find the length of a side of a right triangle using SohCahToa? (Sec 7-4)

Can you find an angle in a right triangle using SohCahToa? (Sec 7-4)

Can you decipher between an angle of elevation and an angle of depression? (Sec 7-5)

Do you know your Law of Sines? (Sec 7-6)

Can you find a side using the Law of Sines? (Sec 7-6)

Can you find an angle using the Law of Sines? (Sec 7-6)

Do you know your Law of Cosines? (Sec 7-7)

Can you find a side using the Law of Cosines? (Sec 7-7)

Can you find an angle using the Law of Cosines? (Sec 7-7)

Chapter 7 Review ⎕ Chapter 7 Study Guide & Review #’s 1-40

⎕ Chapter 7 Practice Test #’s 1- 25

Chapter 7 Project

⎕ Chapter 7 Project (Summative Assessment

Must score > 70.)

Chapter 7 Test

⎕ Chapter 7 Test (Summative Assessment

Must score > 70.)

Geometry Chapter 7 Triple Entry Journal

Word Definition Picture and/or Example

angle of depression

(pg 372)

angle of elevation (pg 371)

geometric mean

(pg 342)

Law of Cosines (pg 385)

Law of Sines (pg 377)

Pythagorean Identity (pg 391)

Pythagorean triple

(pg 352)

solving a triangle (pg 378)

trigonometric ratio

(pg 364)

trigonometry (pg 364)

Sec 7-1 Geometric Mean

Key Points Notes

Geometric Mean

Find the geometric mean between the pair

of numbers.

Find AD.

Example: 2 and 50

Geometric Mean

Formula

Sec 7-2 The Pythagorean Theorem and Its Converse

Key Points Notes

What is the Pythagorean

Theorem?

What does the Pythagorean

Theorem help us find?

When CAN you

use Pythagorean Theorem?

Examples of Pythagorean

Theorem

Using the Converse of the

Pythagorean Theorem

Finding the hypotenuse. Finding a leg.

Determine whether each set of measures are the sides of a right triangle. Explain your work. a) 9, 12, and 15 b) 21, 42, and 54

Sec 7-3 Special Right Triangles

Key Points Notes

What are the special right triangles?

Examples using special right

triangles.

a) b)

c)

Sec 7-4 Trigonometry

Key Points Notes

What does SohCahToa stand

for?

What does SohCahToa help

us find?

When can you use SohCahToa?

Examples using SohCahToa.

Sec 7-5 Angles of Elevation and Depression

Key Points Notes

Angles of elevation and depression

Word problem involving angles of elevation and

depression.

At the circus, a person in the audience at ground level watches the high-wire routine. A 5-foot 6-inch tall acrobat is standing on a platform that is 25 feet off the ground. How far is the audience member from the base of the plat form, if the angle of elevation from the audience member’s line of sight to the top of the acrobat is 27 degrees?

Sec 7-6 The Law of Sines

Key Points Notes

What is the Law of Sines?

(Capital letters

represent ANGLES and

lower case letters are SIDE

LENGTHS.)

Examples using Law of Sines.

Finding a side. Find an angle.

Sec 7-7 The Law of Cosines

Key Points Notes

What is the Law of Cosines?

(Capital letters

represent ANGLES and

lower case letters are SIDE

LENGTHS.)

Examples using Law of Cosines.

Find a side. Finding an angle.

Geometry Chapter 7 Study Guide

Sec 7-1 Geometric Mean

Do you know the geometric mean formula? (Sec 7-1)

Do you know that when you draw an altitude in a right triangle from the right

angle to the hypotenuse, it creates 2 smaller triangles that are similar to the large

triangle? (Sec 7-1)

Can you set up proportions using the situation above? (Sec 7-1)

Sec 7-2 They Pythagorean Theorem and Its Converse

Do you know Pythagorean Theorem? (Sec 7-2)

What does the Pythagorean Theorem help us find? (Sec 7-2)

What does the Converse of the Pythagorean Theorem tell us? (Sec 7-2)

Sec 7-3 Special Right Triangles

Do you know your two special right triangles? (Sec 7-3)

Sec 7-4 Trigonometry

Do you know what SohCahToa means? (Sec 7-4)

Do you know what SohCahToa helps you find? (Sec 7-4)

Can you find the length of a side of a right triangle using SohCahToa? (Sec 7-4)

Can you find an angle in a right triangle using SohCahToa? (Sec 7-4)

Sec 7-5 Angle of Elevation and Depression

Can you decipher between an angle of elevation and an angle of depression?

(Sec 7-5)

Sec 7-6 The Law of Sines

Do you know your Law of Sines? (Sec 7-6)

Can you find a side using the Law of Sines? (Sec 7-6)

Can you find an angle using the Law of Sines? (Sec 7-6)

Sec 7-7 The Law of Cosines

Do you know your Law of Cosines? (Sec 7-7)

Can you find a side using the Law of Cosines? (Sec 7-7)

Can you find an angle using the Law of Cosines? (Sec 7-7)

CSI Geometry: Trigonometry

Geometry ~ Chapter 7 Project ~ Scoring Rubric

Learning Targets

Pythagorean Theorem

Special Right Triangles

Sine, Cosine & Tangent

Law of Sines & Cosines

Angles of Depression and Elevation

Scene Earned Points

Possible Points

What is being scored? Done?

Scene 1

2 pts 2 pts 2 pts

Write out a trigonometry equation.

Plug numbers into your trigonometry equation.

Correctly found the height of the Taj Mahal to the nearest foot.

Scene 2

4 pts 4 pts 4 pts

Showed all your work and solved for x correctly.

Showed all your work and solved for y correctly.

Showed all your work and solved for m correctly.

Scene 3

2 pts

2 pts

2 pts

6 pts

6 pts

Showed all your work and found ALL the angles in 1st triangle.

Showed all your work and found ALL the angles in 2nd triangle.

Answered the question ‘How many of these unknown angles is greater than 50 degrees?’ correctly.

Showed ALL your work and EXPLAINED how you got your final answer.

Showed ALL your work and EXPLAINED how you got your final answer.

Scene 4

4 pts

4 pts

2 pts

Showed all your work and found the length of Cosine Ramp.

Showed all your work and found the length of Sine Ramp.

Answered ‘Which is Longer?’ correctly.

Scene 5

6 pts Showed all your work and found how tall Mt. Everest is to the nearest foot.

Scene 6

6 pts

Showed all your work and found the length of the bridge to the nearest meter.

Cryptic Puzzle Solver Text

Message

2 pts 4 pts

Plugged numbers in correctly.

Showed and EXPLAINED your work and came out with the correct answer.

Case Summary

6 pts

6 pts

6 pts

6 pts

6 pts

6 pts

Prepare a typed case in which you need to demonstrate your understanding of each of the following topics:

Pythagorean Theorem (Find one from this project and one from your book. Explain HOW you did them both.)

Special Right Triangles (Find one from this project and one from your book. Explain HOW you did them both.)

Sine, Cosine & Tangent (Find one from this project and one from your book. Explain HOW you did them both.)

Law of Sine & Cosine (Find one from this project and one from your book. Explain HOW you did them both.)

Angles of Depression and Elevation (find one from this project and one from your book. Explain HOW you did them both.)

What 6 vocabulary words and definitions were necessary throughout this project?

Final Score