📚 Topic Summary
The Pythagorean Theorem is a fundamental concept in geometry that describes the relationship between 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). The converse of the Pythagorean Theorem allows us to determine if a triangle is a right triangle based on the lengths of its sides. These concepts are applied in various real-world scenarios, from construction to navigation.
Let's say the legs of the right triangle are $a$ and $b$, and the hypotenuse is $c$. The Pythagorean Theorem is represented as:
$a^2 + b^2 = c^2$
🧮 Part A: Vocabulary
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. Pythagorean Theorem |
C. Either of the two shorter sides in a right triangle. |
| 4. Right Triangle |
D. A triangle with one angle measuring 90 degrees. |
| 5. Converse of the Pythagorean Theorem |
E. If $a^2 + b^2 = c^2$, then the triangle is a right triangle. |
✍️ Part B: Fill in the Blanks
Complete the paragraph using the words provided: hypotenuse, legs, right, square, triangle.
In a ____ triangle, the Pythagorean Theorem states that the ____ of the ____ of the two ____ is equal to the square of the ____.
🤔 Part C: Critical Thinking
Explain a real-world scenario where you might use the Pythagorean Theorem to solve a problem. Be specific about what you are trying to find.