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Chapter 8: Right Triangles and Trigonometry

Chapter 8: Right Triangles and Trigonometry. Section 8-1: The Pythagorean Theorem and its Converse . Objectives:. To use the Pythagorean Theorem. To use the converse of the Pythagorean Theorem. Vocabulary. Pythagorean Triple. Pythagoras. Greek mathematician from the 6 th century BC.

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Chapter 8: Right Triangles and Trigonometry

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  1. Chapter 8:Right Triangles and Trigonometry Section 8-1: The Pythagorean Theorem and its Converse

  2. Objectives: • To use the Pythagorean Theorem. • To use the converse of the Pythagorean Theorem.

  3. Vocabulary • Pythagorean Triple

  4. Pythagoras • Greek mathematician from the 6th century BC. • Famous for the Pythagorean Theorem • Others knew of the Pythagorean Theorem first: • Babylonians • Egyptians • Chinese

  5. Theorem 8-1:“The Pythagorean Theorem” • In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the hypotenuse.

  6. Pythagorean Triple • A Pythagorean triple is a set of nonzero whole numbers a, b, and c that satisfy the equation:

  7. Example • Solve for the variable. Do the sides of the triangle form a Pythagorean triple? x 20 21

  8. Example • Solve for the variable. Do the sides of the triangle form a Pythagorean triple? 34 16 y

  9. Example • Solve for the variable. Do the sides of the triangle form a Pythagorean triple? 8 z 4

  10. Theorem 8-2:“Converse of the Pythagorean Theorem” • If the square of the lengths of one side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle.

  11. Using the Converse of the Pythagorean Theorem • Is the triangle a right triangle? 10 8 6

  12. Using the Converse of the Pythagorean Theorem • Is the triangle a right triangle? 6 5 2

  13. *Note:If a triangle is not a right triangle, then it is either an acute triangle or an obtuse triangle.

  14. Theorem 8-3: • If the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, then the triangle is obtuse.

  15. Theorem 8-4: • If the square of the length of the longest side of a triangle is less than the sum of the squares of the lengths of the other two sides, then the triangle is obtuse.

  16. Classify the Triangles asAcute, Obtuse, or Right. • 7, 8, and 11 • 16, 19, and 24 • 5, 7, and 10

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