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8-1 The Pythagorean Theorem and Its Converse

8-1 The Pythagorean Theorem and Its Converse. Learning Goal To use the Pythagorean Theorem and its converse. Pythagorean Theorem a 2 + b 2 = c 2. Pythagorean Theorem a 2 + b 2 = c 2 The right angle touches the a and b. Pythagorean Theorem : a 2 + b 2 = 2. c. c. a. b.

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8-1 The Pythagorean Theorem and Its Converse

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  1. 8-1The Pythagorean Theorem and Its Converse

  2. Learning GoalTo use the Pythagorean Theorem and its converse.

  3. Pythagorean Theorema2 + b2 = c2

  4. Pythagorean Theorema2 + b2 = c2The right angle touches the a and b.

  5. Pythagorean Theorem:a2 + b2 = 2 c c a b

  6. Pythagorean Theorem:a2 + b2 = 2 c 5 3 x

  7. Pythagorean Theorem:32+ x2= 2 c 5 3 x

  8. Pythagorean Triples and Their Multiples3, 4, 55, 12, 13

  9. ExampleIs a triangle with side lengths 9, 12 and 16 a right triangle?

  10. ExampleIs a triangle with side lengths 9, 12 and 16 a right triangle?a2 + b2 = c2

  11. ExampleIs a triangle with side lengths 9, 12 and 16 a right triangle?a2 + b2 = c2Which number goes in the c spot?

  12. ExampleIs a triangle with side lengths 9, 12 and 16 a right triangle?a2 + b2 = c2Which number goes in the c spot?Why?

  13. ExampleIs a triangle with side lengths 9, 12 and 16 a right triangle?a2 + b2 = c292 + 122 = 162

  14. ExampleIs a triangle with side lengths 9, 12 and 16 a right triangle?a2 + b2 = c292 + 122 = 16281 + 144 = 256

  15. ExampleIs a triangle with side lengths 9, 12 and 16 a right triangle?a2 + b2 = c292 + 122 = 16281 + 144 = 256225 = 256

  16. ExampleIs a triangle with side lengths 9, 12 and 16 a right triangle?a2 + b2 = c292 + 122 = 16281 + 144 = 256225 = 256No

  17. When you plug the 3 sides of a triangle into the Pythagorean theorem, if the c2 is larger then it is an obtuse triangle. If it is smaller then it is an acute triangle.

  18. Examplea2 + b2 = c292 + 122 = 16281 + 144 = 256225 = 256Is this triangle Acute or Obtuse?

  19. Examplea2 + b2 = c292 + 122 = 16281 + 144 = 256225 = 256Obtuse

  20. Turn to page 495.2, 3, 138-10, 19-30, 33, 36-385 Points: 100% Complete 4 Points: 80% Complete 3 Points: 60% Complete 2 Points: 40% Complete 1 Point: 20% Complete

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