Test questions on deriving a² + b² = c² for middle school math

📚 Quick Study Guide

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• Pythagorean Theorem: In a right-angled triangle, 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.
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• Formula: $a^2 + b^2 = c^2$, where $c$ represents the length of the hypotenuse, and $a$ and $b$ represent the lengths of the other two sides (legs).
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• Applications: Used to find missing side lengths in right triangles, check if a triangle is a right triangle, and in various fields like construction, navigation, and engineering.
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• Key Terms:
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  • Hypotenuse: The longest side of a right triangle, opposite the right angle.
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  • Legs: The two shorter sides of a right triangle that form the right angle.
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• Important Note: The Pythagorean theorem only applies to right-angled triangles.

Practice Quiz

1. Question 1: In a right triangle, if side $a = 3$ and side $b = 4$, what is the length of side $c$?
1. A. 5
2. B. 7
3. C. 25
4. D. 12
2. Question 2: A triangle has sides of length 5, 12, and 13. Is it a right triangle?
1. A. Yes
2. B. No
3. C. Maybe
4. D. Cannot be determined
3. Question 3: If the hypotenuse of a right triangle is 10 and one side is 6, what is the length of the other side?
1. A. 4
2. B. 8
3. C. 16
4. D. 14
4. Question 4: Which of the following sets of side lengths could form a right triangle?
1. A. 2, 3, 4
2. B. 7, 24, 25
3. C. 4, 5, 6
4. D. 1, 2, 3
5. Question 5: A ladder leans against a wall. The ladder is 13 feet long, and the base of the ladder is 5 feet from the wall. How high up the wall does the ladder reach?
1. A. 8 feet
2. B. 12 feet
3. C. 18 feet
4. D. 65 feet
6. Question 6: What is the formula for the Pythagorean theorem?
1. A. $a + b = c$
2. B. $a^2 + b^2 = c^2$
3. C. $a - b = c$
4. D. $a^2 - b^2 = c^2$
7. Question 7: The legs of a right triangle are equal in length. If the hypotenuse is $\sqrt{50}$, what is the length of each leg?
1. A. 5
2. B. 10
3. C. 25
4. D. $\sqrt{25}$