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Name_____________________________________ Class____________________________ Date ________________ Lesson 3-9 The Pythagorean Theorem Lesson Objectives 1 Solve problems using the Pythagorean Theorem 2 Identify right triangles NAEP 2005 Strand: Geometry Topic: Relationships Among Geometric Figures Local Standards: ____________________________________ All rights reserved. Vocabulary and Key Concepts. The Pythagorean Theorem In any right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. 2 2 c a 2 b The Converse of the Pythagorean Theorem If a triangle has sides of lengths a, b, and c, and a2 b2 c2, then the triangle is a with hypotenuse of length c. The hypotenuse is © Pearson Education, Inc., publishing as Pearson Prentice Hall. The legs are A conditional is A hypothesis is A conclusion is A converse is Examples. 1 Using the Pythagorean Theorem What is the length of the hypotenuse of this triangle? a2 b2 c2 2 2 c2 2 c c2 c Substitute for a and c 8m Use the Pythagorean Theorem. for b. 15 m Simplify. Find the principal square root of each side. Simplify. The length of the hypotenuse is 17 m. Daily Notetaking Guide Algebra 1 Lesson 3-9 65 Name_____________________________________ Class____________________________ Date ________________ 2 Using the Converse of the Pythagorean Theorem Determine whether the given lengths are sides of a right triangle. a. 5 in., 5 in., and 7 in. 2 2 2 Determine whether a2 b2 c 2, where c is the longest side. Simplify. This triangle a right triangle. 2 2 Determine whether a2 b2 c2, where c is the longest side. Simplify. This triangle a right triangle. 3 Physics If two forces pull at right angles to each other, the resultant force is Force A eC Force B 2 2 2 2 Determine whether a b c , rc Fo 2 nt ta 2 ul For a 50-lb force and a 120-lb force, the resultant force is 130 lb. Are the forces pulling at right angles to each other? s Re represented as the diagonal of a rectangle, as shown in the diagram. The diagonal forms a right triangle with two of the perpendicular sides of the rectangle. where c is the greatest force. The forces of 50 lb and 120 lb at right angles to each other. Quick Check. 1. What is the length of the hypotenuse of a right triangle with legs of lengths 7 cm and 24 cm? 2. A triangle has sides of lengths 10 m, 24 m, and 26 m. Is the triangle a right triangle? 3. Physics Consider Example 3. For a 70-lb force and a 60-lb force, the resultant force is 100 lb. Are the forces pulling at right angles to each other? 66 Algebra 1 Lesson 3-9 Daily Notetaking Guide © Pearson Education, Inc., publishing as Pearson Prentice Hall. 2 All rights reserved. b. 10 cm, 24 cm, and 26 cm