geometry chapter 7 capacity matrix right triangles and
TRANSCRIPT
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