1. GEOMETRY HELP 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? a 2 + b 2 = c 2 Use the Pythagorean Theorem. 16 2 + 30 2 = c 2 Substitute 16 for a and 30 for b. 256 + 900 = c 2 Simplify. 1156 = c 2 34 = cTake the square root. The length of the hypotenuse is 34. The lengths of the sides, 16, 30, and 34, form a Pythagorean triple because they are whole numbers that satisfy a 2 + b 2 = c 2. Notice that each length is twice the common Pythagorean triple of 8, 15, and 17. Quick Check The Pythagorean Theorem and Its Converse LESSON 8-1 Additional Examples

2. GEOMETRY HELP a 2 + b 2 = c 2 Use the Pythagorean Theorem. x 2 + 10 2 = 12 2 Substitute x for a, 10 for b, and 12 for c. x 2 + 100 = 144 Simplify. x 2 = 44Subtract 100 from each side. x = 4(11) Take the square root of each side. x = 2 11 Simplify. Find the value of x. Leave your answer in simplest radical form. The Pythagorean Theorem and Its Converse LESSON 8-1 Additional Examples Quick Check

3. GEOMETRY HELP a 2 + b 2 = c 2 Use the Pythagorean Theorem. 90 2 + 90 2 = c 2 Substitute 90 for a and for b. 8100 + 8100 = c 2 Simplify. The distance to home plate from second base is about 127 ft. Use the information to draw a baseball diamond. A baseball diamond is a square with 90-ft sides. Home plate and second base are at opposite vertices of the square. About how far is home plate from second base? 16,200 = c 2 The Pythagorean Theorem and Its Converse LESSON 8-1 Additional Examples Quick Check c = 16,200 Take the square root. c Use a calculator.

4. GEOMETRY HELP Is this triangle a right triangle? 52 ≠ 49 Because a 2 + b 2 ≠ c 2, the triangle is not a right triangle. a 2 + b 2 c 2 4 2 + 6 2 7 2 Substitute 4 for a, 6 for b, and 7 for c. 16 + 36 49 Simplify. The Pythagorean Theorem and Its Converse LESSON 8-1 Additional Examples Quick Check

5. GEOMETRY HELP The numbers represent the lengths of the sides of a triangle. Classify each triangle as acute, obtuse, or right. a.15, 20, 25 c 2 a 2 + b 2 Compare c 2 with a 2 + b 2. 625 225 + 400 Simplify. 625 = 625 Because c 2 = a 2 + b 2, the triangle is a right triangle. 25 2 15 2 + 20 2 Substitute the greatest length for c. The Pythagorean Theorem and Its Converse LESSON 8-1 Additional Examples

6. GEOMETRY HELP (Continued) b. 10, 15, 20 400 325 Because c 2 a 2 + b 2, the triangle is obtuse. 20 2 10 2 + 15 2 Substitute the greatest length for c. 400 100 + 225 Simplify. c 2 a 2 + b 2 Compare c 2 with a 2 + b 2. The Pythagorean Theorem and Its Converse LESSON 8-1 Additional Examples Quick Check