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

11. Question 11 Find the length of the missing side. 3 in 5 in a 2 + b 2 = c 2 3 2 + 5 2 = c 2 9 + 25 = c 2 34 = c 2 5.8 in = c

12. Questions 12 & 13

13. Questions 14, 15, & 16 Explain what the word volume means. The measure of the space occupied by a solid How does the volume of a cylinder compare to the volume of a cone? The volume of a cylinder is three times greater than the volume of a cone How does the volume of a cylinder and cone compare to the volume of a sphere? The volume of a sphere is double the volume of a cone

14. Question 17 A candle maker uses a cylinder mold, which is 18 inches tall and has a radius of 1 inch. What is the volume of the candle mold? 18 in. r = 1 in.

15. Question 18 A party hat is in the shape of a cone with a radius of 3 in. and a height of 5 in. What is the volume of the party hat? r = 3 in. 5 in.

16. Question 19 What is the volume of a beach ball with a radius of 12 centimeters? r = 12 cm

17. Question 20 What is the volume of the following cone?

18. Question 21 Find the volume of the sphere shown below.

19. Question 22 Find the volume of the cylinder below.

20. Question 23 r = ? m h = 1 m

21. Question 24 What are the two methods of finding the distance between two points? Given two points, you can always plot them, draw the right triangle, and then find the length of the hypotenuse. The length of the hypotenuse is the distance between the two points. Another way to find the distance between two points is algebraically with a formula.

22. Question 25 What is the distance between P1 and P2? 9 units 6 units The legs are 6 and 9, now I can find the distance by finding the hypotenuse of the triangle: a 2 + b 2 = c 2 6 2 + 9 2 = c 2 36 + 81 = c 2 117 = c 2 10.8 = c

23. Question 26 What is the distance between P1 and P2? 3 units 4 units The legs are 3 and 4, now I can find the distance by finding the hypotenuse of the triangle: a 2 + b 2 = c 2 3 2 + 4 2 = c 2 9 + 16 = c 2 25 = c 2 5 = c

24. Question 27 Given points C(-6, 10) and D(-3, -2), what is the length of CD?

25. Question 28 Given points S(-4, -2) and T(-1, 0), what is the length of ST?