5 7 The The Pythagorean Theorem Warm Up

5 -7 The The. Pythagorean. Theorem Warm Up Lesson Presentation Lesson Quiz Holt. Mc. Dougal Geometry Holt

5 -7 The Pythagorean Theorem Warm Up Classify each triangle by its angle measures. 1. 2. acute 3. Simplify right 12 4. If a = 6, b = 7, and c = 12, find a 2 + b 2 and find c 2. Which value is greater? 85; 144; c 2 Holt Mc. Dougal Geometry

5 -7 The Pythagorean Theorem Objectives Use the Pythagorean Theorem and its converse to solve problems. Use Pythagorean inequalities to classify triangles. Holt Mc. Dougal Geometry

5 -7 The Pythagorean Theorem Vocabulary Pythagorean triple Holt Mc. Dougal Geometry

5 -7 The Pythagorean Theorem is probably the most famous mathematical relationship. As you learned in Lesson 1 -6, it states that in a right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse. a 2 + b 2 = c 2 Holt Mc. Dougal Geometry

5 -7 The Pythagorean Theorem A set of three nonzero whole numbers a, b, and c such that a 2 + b 2 = c 2 is called a Pythagorean triple. Holt Mc. Dougal Geometry

5 -7 The Pythagorean Theorem The converse of the Pythagorean Theorem gives you a way to tell if a triangle is a right triangle when you know the side lengths. Holt Mc. Dougal Geometry

5 -7 The Pythagorean Theorem You can also use side lengths to classify a triangle as acute or obtuse. B c A Holt Mc. Dougal Geometry a b C

5 -7 The Pythagorean Theorem To understand why the Pythagorean inequalities are true, consider ∆ABC. Holt Mc. Dougal Geometry

5 -7 The Pythagorean Theorem Remember! By the Triangle Inequality Theorem, the sum of any two side lengths of a triangle is greater than the third side length. Holt Mc. Dougal Geometry

5 -7 The Pythagorean Theorem Example 4 A: Classifying Triangles Tell if the measures can be the side lengths of a triangle. If so, classify the triangle as acute, obtuse, or right. 5, 7, 10 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. Holt Mc. Dougal Geometry

5 -7 The Pythagorean Theorem Example 4 A Continued Step 2 Classify the triangle. c 2 102 ? = a 2 + b 2 ? = 52 + 72 ? Compare c 2 to a 2 + b 2. Substitute the longest side for c. 100 = 25 + 49 Multiply. 100 > 74 Add and compare. Since c 2 > a 2 + b 2, the triangle is obtuse. Holt Mc. Dougal Geometry