The Pythagorean Theorem is a fundamental concept in geometry that describes the relationship between the sides of a right triangle. Specifically, it states that the sum of the squares of the two shorter sides (legs or cathetus) of a right triangle is equal to the square of the longest side (hypotenuse). This theorem is crucial for solving many geometric problems and has various real-world applications.
This worksheet provides you with exercises to practice formulating equations based on the Pythagorean Theorem. You'll learn to identify the sides of a right triangle and set up the equation $a^2 + b^2 = c^2$ correctly, where $c$ represents the hypotenuse, and $a$ and $b$ represent the other two sides.
Match the terms with their definitions:
| Term | Definition |
|---|---|
| 1. Hypotenuse | A. The side opposite the right angle in a right triangle. |
| 2. Leg (Cathetus) | B. The theorem stating $a^2 + b^2 = c^2$ for a right triangle. |
| 3. Right Triangle | C. Either of the two shorter sides of a right triangle that form the right angle. |
| 4. Pythagorean Theorem | D. A triangle that contains one 90-degree angle. |
| 5. Square | E. The result of multiplying a number by itself. |
Complete the following paragraph with the correct words:
The Pythagorean Theorem applies only to _____ triangles. It states that the _____ of the hypotenuse is equal to the sum of the _____ of the other two sides, which are called _____. Therefore, if we know the lengths of two sides, we can find the length of the _____ side.
Explain in your own words why it is important to correctly identify the hypotenuse when applying the Pythagorean Theorem.
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