The Pythagorean Theorem describes the relationship between the sides of a right-angled triangle. It 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. This can be written as $a^2 + b^2 = c^2$, where 'a' and 'b' are the lengths of the legs, and 'c' is the length of the hypotenuse.
This worksheet will help you understand how to apply the Pythagorean Theorem to find missing side lengths in right triangles and solve related problems. Let's get started!
Match the terms with their correct definitions:
| Term | Definition |
|---|---|
| 1. Hypotenuse | A. The side opposite the right angle in a right triangle. |
| 2. Leg | B. The longest side of a right triangle. |
| 3. Right Angle | C. An angle measuring 90 degrees. |
| 4. Pythagorean Theorem | D. $a^2 + b^2 = c^2$ |
| 5. Square Root | E. A value that, when multiplied by itself, gives the original number. |
Complete the following paragraph using the words provided (Hypotenuse, Legs, Right Triangle, Pythagorean Theorem, Square).
The _________ states that in a _________, the _________ of the _________ of the _________ is equal to the sum of the squares of the other two _________.
Explain, in your own words, why the Pythagorean Theorem only works for right triangles. Use examples to support your explanation.
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