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Pythagorean Triples and Inequality Theorem

Pythagorean Triples and Inequality Theorem. Students will be able to identify a Pythagorean triple and classify a triangle using the Pythagorean Inequality Theorem. Pythagorean Triples.

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Pythagorean Triples and Inequality Theorem

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  1. Pythagorean Triples and Inequality Theorem Students will be able to identify a Pythagorean triple and classify a triangle using the Pythagorean Inequality Theorem

  2. Pythagorean Triples • A set of three nonzero whole numbers a, b and c such that a2 + b2 = c2 is called a Pythagorean triple. • These are some common Pythagorean triples: • How can we identify a Pythagorean triple? • Use the Pythagorean Theorem to make sure all threenumbers are wholenumbers 3, 4, 55, 12, 138, 15, 177, 24, 25 Unit E

  3. Identifying Pythagorean Triples Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain. a2+ b2 = c2 142+ 482 = c2 2500 = c2 50 = c The side lengths are nonzero whole numbers that satisfy the equation a2 + b2 = c2, so they form a Pythagorean triple. Unit E

  4. Pythagorean Inequalities Theorem In ABC, c is the length of the longest side. • If c2 < a2 + b2, then ΔABC is an acute triangle. • If c2 > a2 + b2, then ΔABC is an obtuse triangle. Unit E

  5. ? c2=a2+b2 ? 102= 52+ 72 ? 100 = 25 + 49 Example of Classifying Triangles Tell if the measures 5, 7 and 10 can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right. Step 1: Determine if the measures form a triangle. By the Triangle Inequality Theorem, 5, 7, and 10 can be the side lengths of a triangle. Step 2: Classify the triangle. 100 > 74 Since c2>a2+b2, the triangle is obtuse. Unit E

  6. Lesson Quiz • Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain. • Tell if the measures 9, 13, and 15 can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right. 13; yes; the side lengths are nonzero whole numbers that satisfy Pythagorean’s Theorem. yes; acute Unit E

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