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# What's so special about similar right triangles?

Lesson 1 of 17

## Objective: SWBAT identify the relationships between the ratios of side lengths of similar triangles.

## Big Idea: The properties of similar triangles are established as a basis to learn right triangle trigonometry.

*50 minutes*

To warm-up for today’s lesson, I ask students to review basic right triangle properties. I present the clicker question on page 2 of Flipchart_Special Triangles Day 1. In this task students are asked to find missing side lengths of a right triangle. Then, on page 3 of the Flipchart students are asked to recall the sum of the interior angles of a triangle. After students have responded, I plan to review the correct answers to insure students are ready for today’s activity. As students will need to know how to calculate the missing side lengths of right triangles as well as identify the value of missing interior angles in today's lesson.

I know these problems are very basic. Students should already be coming to us with these skills, but I have found in the past that my students forget these basic facts about right triangles and they are essential to being successful in today's activity. Hopefully, as the Common Core era progresses and my students build a greater depth of understanding and have better retention these basic problems will be cut so we can spend more time on the next activity.

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In today's investigation students review attributes of right triangles and similar triangles as we prepare to build on this knowledge during the unit. I describe the flow of the lesson in the Investigation Overview video. To complete the Similar Right Triangles investigation, students need the following resources: centimeter graph paper, a protractor, straight edges, and a calculator.

As I state in the video, I will allow students to work independently and make choices about which resources they will use to complete the investigation. I will be paying conscious attention to the Mathematical Practices that the students demonstrate as they work. At this stage of the curriculum, it is important that students demonstrate proficiency with mathematical practices as they complete tasks like today's investigation.

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#### Closure: 3W's

*5 min*

To close out today’s lesson I want students to take a moment to reflect individually on what they learned today. Present page 4 of the Flipchart_Special Triangles Day 1. On a sheet of paper, which they will turn in, students should complete a **3 W’s Closure.**

The three W’s they will answer are:

- What did we learn today?
- Why do you think we learned this?
- Where are we going with this?

#### Resources

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*Responding to Michael Link*According to the Flipchart, this used to be unit 7. I'm guessing that Unit 7 was simply replaced by the Rotations and Cyclical Functions unit. Perhaps it was better suited to the cohesiveness of the course. | 11 months ago | Reply

*Responding to Michael Link*I'm guessing that it was a unit that used to be in the course but was decided to be unnecessary? And I'm guessing that she left it in because it could be useful if a teacher decides that it is necessary? This is just my speculation of course, but I did this entire curriculum last year and did NOT do this unit. The students did completely fine and did not seem to need it. | 11 months ago | Reply

I noticed that the Fundamentals of Trig Unit is after the Final Exam. Is this a mistake?

| 2 years ago | Reply*expand comments*

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- UNIT 1: Basic Functions and Equations
- UNIT 2: Polynomial Functions and Equations
- UNIT 3: Rational Functions and Equations
- UNIT 4: Exponential Functions and Equations
- UNIT 5: Logarithmic Functions and Equations
- UNIT 6: Conic Sections
- UNIT 7: Rotations and Cyclical Functions
- UNIT 8: Cyclical Patterns and Periodic Functions
- UNIT 9: Trigonometric Equations
- UNIT 10: Matrices
- UNIT 11: Review
- UNIT 12: Fundamentals of Trigonometry

- LESSON 1: What's so special about similar right triangles?
- LESSON 2: Calculator Investigation: Special Right Triangles (Day 1 of 2)
- LESSON 3: Calculator Investigation: Special Right Triangles (Day 2 of 2)
- LESSON 4: Using Trigonometric Ratios (Day 1 of 2)
- LESSON 5: Using Trigonometric Ratios (Day 2 of 2)
- LESSON 6: Clinometer Project (Day 1 of 2)
- LESSON 7: Clinometer Project (Day 2 of 2)
- LESSON 8: Applications of Right Triangle Trig
- LESSON 9: Law of Sines Basics
- LESSON 10: Ambigouous Cases of the Law of Sines
- LESSON 11: Law of Cosines
- LESSON 12: Short Lesson: Quick Clicker Quizzes
- LESSON 13: More on the Laws: Real World Application
- LESSON 14: Trig Jeopardy
- LESSON 15: Fundamentals of Trig Review - Day 1 of 2
- LESSON 16: Fundamentals of Trig Review - Day 2 of 2
- LESSON 17: Fundamentals of Trigonometry Unit Assessment