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Pythagorean Theorem and Its Converse

Pythagorean Theorem and Its Converse. Chapter 8 Section 1. Objective. Students will use the Pythagorean Theorem and its converse. Pythagorean Theorem (8-1).

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Pythagorean Theorem and Its Converse

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  1. Pythagorean Theorem and Its Converse Chapter 8 Section 1

  2. Objective • Students will use the Pythagorean Theorem and its converse.

  3. Pythagorean Theorem (8-1) • If a triangle is a right triangle, then the sum of the squares of the lengths of the legs is equal to the square of the length o the hypotenuse. • A2 + B2 = C2

  4. Pythagorean Triple • A set of nonzero whole numbers a, b, and c that satisfy the equation a2 + b2 = c2. • Any set of numbers that can be the side lengths of a right triangle

  5. Turn to page 492… • Look at Problem 1,2,3… • Try the “Got It” problems for those examples.

  6. Converse of the Pythagorean Theorem (8-2) • If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangles is a right triangle.

  7. 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.

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

  9. On page 495… • Try problems #1-6 on your own.

  10. Beginning on page 495… • Complete problems #7-38.

  11. Reflection/Exit Slip • What is the Pythagorean Theorem • Knowing what you know about congruent and similar triangles, when might you use the Pythagorean Theorem to solve a problem?

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