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Section 7 – 2 The Pythagorean theorem & Its converse Objectives: To use the Pythagorean Theorem To use the Converse of the Pythagorean Theorem Pythagorean Theorem 2 2 + = 2 Used to find a missing side of a RIGHT triangle. Pythagorean Triple A set of nonzero whole numbers a, b, and c that satisfy the Pythagorean Theorem. 3, 4, 5 Common Pythagorean Triples: 5, 12, 13 8, 15, 17 7, 24, 25 If you multiply each number in a Pythagorean Triple by the same whole number, the three numbers that result also form a Pythagorean Triple Example 1 A) Pythagorean Triples Find the length of the hypotenuse of ∆ABC. Do the lengths of the sides of ∆ABC form a Pythagorean Triple? B) A right triangle has a hypotenuse of length 25 and a leg of length 10. Find the length of the other leg. Do the lengths of the sides form a Pythagorean triple? C) A right triangle has legs of length 16 and 30. Find the length of the hypotenuse. Do the lengths of the sides form a Pythagorean triple? Example 2 Using Simplest Radical Form A) Find the value of x. Leave your answer in simplest radical form. B) The hypotenuse of a right triangle has length 12. One leg has length 6. Find the length of the other leg. Leave your answer in simplest radical form. C) Find the value of x. Leave your answer in simplest radical form. Example 3 Real-World Connection A) The Parks Department rents paddle boats at docks near each entrance to the park. About how far is it to paddle from one dock to the other? B) How far is home plate from second base on a baseball diamond? C) How far is home plate from second base on a softball diamond? Textbook Page 360 – 361; #1 – 17 Section 7 – 2 Continued… Objectives: To use the Converse of the Pythagorean Theorem Example 4 A) Finding Area Find the area of the triangle. B) Find the area of the triangle. C) The hypotenuse of an isosceles right triangle has length 20 cm. Find the area. Converse of the Pythagorean Theorem If the square of the length of one side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle. Example 5 Is it a Right Triangle? Is each triangle a right triangle? A) B) C) A triangle with side lengths 16, 48, and 50. Theorem 7 – 6 2 2 2 If > + , the triangle is ________ Theorem 7 – 7 If 2 < 2 + 2 , the triangle is ________ Example 6 Classifying Triangles as Acute, Obtuse, or Right. The lengths of the sides of a triangle are given. Classify each triangle as acute, obtuse, or right. A) 6, 11, 14 B) 12, 13, 15 C) 7, 8, 9 Homework: 7 – 2 Ditto; 1 – 19 Odds