Triangles And the Pythagorean Theorem Practice Questions

Review the following concept if necessary: Triangles and the Pythagorean Theorem Study Guide.

Triangles And the Pythagorean Theorem Practice Questions

Problems

ΔABC is a right triangle.

1. Name the legs.
2. Name the hypotenuse.

ΔPQR is a right triangle.



3. Name the legs.
4. Name the hypotenuse.

ΔHLM is a right triangle.



5. Name the legs.
6. Name the hypotenuse.

7. Complete the chart.

Find each missing length.

8. 
9. 
10. 

Use this parallelogram to answer questions 11 and 12.



11. Determine x.
12. Using the information given, determine y².

The lengths of three sides of a triangle are given. Determine whether the triangles are right triangles.

13. 
14. 
15. 25, 24, 7
16. 5, 7, 9
17. 15, 36, 39
18. 9, 40, 41

The lengths of the three sides of a triangle are given. Classify each triangle as acute, right, or obtuse.

19. 30, 40, 50
20. 10, 11, 13
21. 2, 10, 11
22. 7, 7, 10
23. 50, 14, 28
24. 5, 6, 7
25. 8, 12, 7

Julie drew the following star, and wanted to know more about the properties of some of the triangles she created in the process. Use the Pythagorean theorem and the concepts of the lesson to answer questions 26 and 27.



26. = 41 cm and = 9 cm. Find and determine the type of triangle.
27. = 36 ft. and = 27 ft. Find and determine the type of triangle.

Use the following figure to answer question 28–30.



28. How far up a building will an 18-foot ladder reach if the ladder's base is 5 feet from the building? Express your answer to the nearest foot. Solve the problem when the ladder is 3 feet from the building. Why would it be impractical to solve the problem if the base of the ladder was closer than 3 feet from the building?
29. If instead of an 18-foot ladder, a 25-foot ladder was used, how far would the ladder need to be from the base of the building in order for it to reach a window that is 20 feet from the ground?
30. If a ladder is going to be placed 6 feet from the base of the wall and needs to reach a window that is 8 feet from the ground, how long must the ladder be?

Answers

1. and
2. 
3. and
4. 
5. and
6. 
7. 
8. 25
9. 9
10. 8
11. 4
12. 178
13. yes
14. no
15. yes
16. no
17. yes
18. yes
19. right
20. acute
21. obtuse
22. obtuse
23. obtuse
24. acute
25. obtuse
26. = 40 cm, right triangle
27. = 45 ft., right triangle
28. When the ladder is placed 5 feet from the building, the ladder extends a little over 17 feet up the building. When the ladder is placed 3 feet from the building, it reaches about feet up the building. It would be impractical to place the ladder that close or even closer because it would not be stable.You would not go very far up the ladder before you would be falling back down!
29. The ladder would need to be 15 feet from the base of the wall. (15² + 20² = 25²)
30. The ladder would need to be 10 feet tall. (6² + 8² = 10²)