Pythagorean Theorem Worksheet Answer Key
Are you struggling to help your students master the Pythagorean Theorem? Do you need a comprehensive answer key to assess their understanding? Look no further! This Pythagorean Theorem worksheet answer key provides detailed solutions to help you evaluate your students’ knowledge.
What is the Pythagorean Theorem?
The Pythagorean Theorem is a fundamental concept in geometry that describes the relationship between the lengths of the sides of a right-angled triangle. The theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Pythagorean Theorem Formula
The formula for the Pythagorean Theorem is:
a² + b² = c²
where:
- a is the length of one side (usually the base)
- b is the length of the other side (usually the height)
- c is the length of the hypotenuse (the side opposite the right angle)
Worksheet Answer Key
Here are the answers to a sample Pythagorean Theorem worksheet:
| Question # | Problem | Solution |
|---|---|---|
| 1 | In a right-angled triangle, the length of the base is 5 cm and the height is 12 cm. Find the length of the hypotenuse. | c = √(5² + 12²) = √(25 + 144) = √169 = 13 cm |
| 2 | Find the length of the missing side in the triangle with sides 8 cm, 15 cm, and x cm. | a² + b² = c² → 8² + x² = 15² → 64 + x² = 225 → x² = 161 → x = √161 ≈ 12.68 cm |
| 3 | In a right-angled triangle, the length of the hypotenuse is 20 cm and one side is 16 cm. Find the length of the other side. | a² + b² = c² → 16² + b² = 20² → 256 + b² = 400 → b² = 144 → b = √144 = 12 cm |
| 4 | Find the length of the missing side in the triangle with sides 10 cm, 24 cm, and x cm. | a² + b² = c² → 10² + x² = 24² → 100 + x² = 576 → x² = 476 → x = √476 ≈ 21.82 cm |
| 5 | In a right-angled triangle, the length of the base is 7 cm and the hypotenuse is 25 cm. Find the length of the other side. | a² + b² = c² → 7² + b² = 25² → 49 + b² = 625 → b² = 576 → b = √576 = 24 cm |
Tips and Tricks
Here are some tips and tricks to help your students master the Pythagorean Theorem:
- Read the problem carefully: Make sure your students read the problem carefully and understand what is being asked.
- Use the formula: Encourage your students to use the Pythagorean Theorem formula to solve problems.
- Check their work: Encourage your students to check their work by plugging their answers back into the formula.
- Practice, practice, practice: Provide your students with plenty of practice problems to help them master the Pythagorean Theorem.
📝 Note: Encourage your students to show their work and explain their reasoning when solving problems.
What is the Pythagorean Theorem used for?
+The Pythagorean Theorem is used to find the length of the hypotenuse of a right-angled triangle, given the lengths of the other two sides.
Can the Pythagorean Theorem be used for non-right triangles?
+No, the Pythagorean Theorem can only be used for right-angled triangles.
How can I help my students remember the Pythagorean Theorem formula?
+You can help your students remember the formula by creating a mnemonic device, such as "A² + B² = C²" or by having them practice reciting the formula regularly.
By following these tips and using this worksheet answer key, your students will be well on their way to mastering the Pythagorean Theorem.
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