The Pythagorean Theorem is a fundamental concept in geometry that relates the sides of a right triangle. 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 relationship can be expressed 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. Real-world problems involving the Pythagorean Theorem often involve finding distances, heights, or lengths in situations where right triangles can be identified.
This worksheet will help you practice applying the Pythagorean Theorem to solve real-world problems. You'll reinforce your understanding through vocabulary exercises, fill-in-the-blank questions, and a critical thinking challenge. Good luck! 👍
Match the terms with their definitions:
| Term | Definition |
|---|---|
| 1. Hypotenuse | A. The side opposite the right angle in a right triangle. |
| 2. Leg (of a right triangle) | B. A line segment extending from one vertex to the opposite side. |
| 3. Pythagorean Theorem | C. In a right triangle, $a^2 + b^2 = c^2$. |
| 4. Right Triangle | D. A triangle with one 90-degree angle. |
| 5. Altitude | E. Either of the two shorter sides of a right triangle. |
Complete the following paragraph with the correct words.
The Pythagorean Theorem applies only to __________ triangles. The longest side of the triangle is called the __________, which is always opposite the __________ angle. If the lengths of the two legs are $a$ and $b$, and the length of the hypotenuse is $c$, then the theorem can be written as $a^2 + b^2 = __________. Solving real-world problems often involves identifying a __________ triangle within the situation.
Explain how the Pythagorean Theorem can be used in construction or architecture. Provide a specific example.
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