Understanding the Pythagorean Theorem and Its Applications

The page introduces the fundamental concept of the Pythagorean theorem and its practical applications in right triangles. This mathematical principle is demonstrated through detailed examples showing both direct application and its converse.

Definition: The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (BC²) equals the sum of squares of the other two sides (AB² + AC²).

Example: In an exercice pratique théorème de Pythagore rectangle en A, with sides AB = 2cm and AC = 3cm, the hypotenuse BC is calculated as follows: BC² = 2² + 3² = 13 BC = √13 cm ≈ 3.6cm

Highlight: The converse of the theorem is equally important, allowing verification of whether a triangle is right-angled by checking if BC² = AB² + AC².

Vocabulary:

• Hypotenuse: The longest side of a right triangle, opposite to the right angle
• Right angle: An angle measuring 90 degrees
• Square root (√): A mathematical operation to find a number which, when multiplied by itself, gives the original number

Example: A second example demonstrates the converse theorem with sides 3cm, 4cm, and 5cm, proving the triangle is right-angled as 5² = 3² + 4² (25 = 25).