1. Unit 3 - Study Guide

2. Questions 1 & 2 The Pythagorean Theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. The Pythagorean Theorem can be represented by the equation a 2 + b 2 = c 2, where a and b are the length of the legs of the triangle, and c is the length of the hypotenuse.

3. Question 3 Use what you know about the Pythagorean Theorem to label the sides of the following triangle. hypotenuse leg

4. Question 4 Is a triangle with the lengths 7, 24, and 25 a right triangle. Why or why not. Show work to indicate how you got your answer. Use the Pythagorean Theorem to determine if this is a right triangle. 7 2 + 24 2 = 25 2 49 + 576 = 625 625 = 625 The sum of the squares of the legs is equal to the square of the hypotenuse, so it is a right triangle.

5. Question 5 A football field is 360 feet by 45 feet. How long is the walk from one corner diagonally to the opposite corner? 360 ft 45 ft 45 2 + 360 2 = c 2 2025 + 129600 = c 2 131625 = c 2 362.8 ft = c

6. Question 6 Using the illustration below, what is the approximate height of the hot air balloon? a 2 + 1325 2 = 2000 2 a 2 + 1755625 = 4000000 a 2 = 2244375 a = 1498.1 ft

7. Question 7 A rectangle has a diagonal 25 inches long and a width of 6 inches. What is the length of the rectangle? 6 in 25 in 6 2 + b 2 = 25 2 36 + b 2 = 625 b 2 = 589 b = 24.3 in.

8. Question 8 Which of the following measures are valid measures of the sides of a right triangle? Explain your reasoning. A.3, 4, 7 B.5, 12, 13 C.20, 21, 28 D.12, 37, 34 5, 12, and 13 are valid measures of a right triangle because they form a Pythagorean Triple

9. Question 9

10. Question 10 A package is in the shape of a cube. The height if the package is 10 inches. What is the diagonal length of the package? 10 in