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Pythagorean Theorem and It’s Converse

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. Pythagorean Theorem. 25. 9. 16.

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Pythagorean Theorem and It’s 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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