Pythagorean Theorem Explained
This page provides a clear explanation and example of the théorème de Pythagore. It demonstrates how to apply the theorem to solve for the length of the hypotenuse in a right-angled triangle.
The page presents a right-angled triangle ABC, where angle B is the right angle. The lengths of two sides are given: AB = 3 cm and BC = 4 cm. The goal is to find the length of AC, which is the hypotenuse.
Definition: The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides.
The solution is presented step-by-step:
- The theorem is stated algebraically: AC² = AB² + BC²
- The known values are substituted: AC² = 3² + 4²
- The squares are calculated: AC² = 9 + 16
- The sum is found: AC² = 25
- The square root is taken to find AC: AC = √25
- The final answer is given: AC = 5 cm
Example: In this triangle, AB = 3 cm and BC = 4 cm. Using the Pythagorean theorem, we can calculate that AC = 5 cm.
Highlight: The hypotenuse is always the longest side of a right-angled triangle and is opposite the right angle.
This example effectively illustrates the application of the théorème de Pythagore and demonstrates its usefulness in solving geometric problems. It's an essential concept for students preparing for exams like the brevet and is frequently featured in exercices Pythagore 3ème and exercices Pythagore 4ème.
