Page 1: The Pythagorean Theorem and Its Converse

This page introduces the fundamental concepts of the Pythagorean theorem and its practical applications in geometric problem-solving. The content focuses on démonstration de triangle rectangle avec Pythagore through detailed examples.

Definition: In a right triangle with angle A, the square of the hypotenuse (BC²) equals the sum of squares of the other two sides (AC² + AB²).

Example: A practical application is shown with triangle RST, where students must calculate the length of ST. The solution demonstrates the systematic application of the theorem:

1. Given a right triangle at R
2. Using ST² = RT² + RS²
3. Calculating ST² = 28² + 21²
4. Finding ST = 3.5 cm

Highlight: The page introduces the converse of the Pythagorean theorem, showing how it can be used to prove whether a triangle is right-angled.

Vocabulary:

• Théorème de Pythagore: Pythagorean theorem
• Triangle rectangle: Right triangle
• Réciproque: Converse