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Pythagorean Theorem Exploration: Learning, Applying, and Applying Its Converse

Dive into the principles and applications of the Pythagorean Theorem and its converse in this comprehensive exploration. Discover various proofs, Pythagorean triples, coordinate geometry verification, and triangle classifications. Complete with practice questions and real-world applications.

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Pythagorean Theorem Exploration: Learning, Applying, and Applying Its Converse

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  1. You have not lived a perfect day, unless you've done something for someone who will never be able to repay you. -- Ruth Smeltzer Pythagorean Theorem and It’s Converse Chapter 8 Section 2 Learning Goal: Learn/Apply the Pythagorean Th. and it’s converse

  2. Pythagorean Theorem 25 9 16 There are at least 80 different ways to prove the Pythagorean theorem Link to AgileMinds #13, Patty Paper Proof, 1-8

  3. Pythagorean Theorem • Find the missing measures 12.7 √27

  4. Converse of the Pythagorean Th. Determine whether the sides of these triangles could form a right triangle • 9, 12, 15 • 4√3, 4, 8 • 5, 8, 9 yes yes no

  5. Coordinate Geometry • Verify that ∆ABC is a right ∆

  6. Pythagorean Triple • A Pythagorean Triple is three whole numbers that satisfy the equation a2 + b2 = c2 . (Remember our answers from before) • 9, 12, 15 • 4√3, 4, 8 • 5, 8, 9 Are each of these 3 numbers a Pythagorean Triple? rt. ∆ Yes rt. ∆ No not a rt. ∆ No The most common Pythagorean Triple = 3-4-5

  7. Pythagorean Triple Determine whether 30, 40, and 50are the sides of a right triangle. Then state whether they form a Pythagorean triple. Yes, and Yes

  8. Closer Look 12 6 8 9 6 8 • What do we know about a triangle with sides: • 6, 8, 10? • 6, 8, 12? • 6, 8, 9? 10 6 Right Triangle 36 + 64 = 100 8 Obtuse Triangle 36 + 64 < 144 Acute Triangle 36 + 64 > 81

  9. Converse of Pythagorean Th. a2 + b2 = c2  Right Angle c2 > a2 + b2 c2 < a2 + b2 Obtuse Angle Acute Angle What about . . . 1. 2, 3, 4 2. 7, 8, 5√3 > 42 32 + 22 Obtuse ∆ < 5√372 + 82 Acute ∆

  10. Homework • Pythagorean Theorem and Its Converse Worksheet

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