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Understanding the Pythagorean Theorem: Trig Ratios and Proofs

In today’s lesson, we will focus on using trigonometric ratios to find missing side lengths, specifically with a right triangle where one side is 9 and the angle is 39 degrees. We'll also review quiz answers and discuss expectations for the Skate Park Project due Thursday. Our main goal is to deepen our understanding of the Pythagorean Theorem, a² + b² = c², and its validity for right triangles. Students will analyze proof constructions, compare methods from different classmates, and produce a comprehensive solution.

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Understanding the Pythagorean Theorem: Trig Ratios and Proofs

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Presentation Transcript

  1. Warm Up Tuesday, October 22nd A Write the correct Trig Ratio to find the missing side length Find the missing side length 9 x 39˚ B C

  2. Quiz Answers and Scores 4 pts each

  3. Skate Park Projectdue Thursday Quiz Grade

  4. Today’s Goal Task Understand it a little better…

  5. Proofs of the Pythagorean Theorem Remember: a²+b²=c²

  6. Discussion Questions • For what kind of triangles is the Pythagorean Theorem True? • Is it true for any right triangle?

  7. Constructing a Proof • Describe how the blue triangle has moved • Watch what makes a square and what the side lengths are • Remember a squares side length is always sidelength²

  8. A Few More Animations…..

  9. Analyzing and Comparing • Describe what each student has done. • Will the approach lead to a proof of the theorem? • Explain how the work can be improved. • Compare the three solutions. • Whose solution method do you find most convincing? Why? • Produce a complete correct solution using your preferred method.

  10. Penelope’s Method

  11. Nadia’s Method

  12. Sophie’s Method

  13. Proving the Pythagorean Theorem (revisited)

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