Understanding the Converse of Pythagorean Theorem
The first page introduces the fundamental concept of verifying whether a triangle is right-angled using the converse of the Pythagorean theorem. This mathematical principle examines the relationship between the squares of a triangle's sides.
Definition: The converse of the Pythagorean theorem states that if the square of the longest side (hypotenuse) equals the sum of squares of the other two sides, then the triangle must be right-angled.
Example: A triangle with sides measuring 13 cm, 11 cm, and 7 cm is analyzed:
- CB² = 13² = 169 cm²
- CA² + BA² = 11² + 7² = 170 cm² Since 169 ≠ 170, the triangle is not right-angled.
Highlight: All side lengths must be known to apply this theorem effectively.
Vocabulary:
- Hypotenuse: The longest side of a right triangle, opposite to the right angle
- Pythagorean equality: The mathematical relationship where a² + b² = c² in a right triangle
Quote: "L'égalité de Pythagore n'est pas vérifiée : CB² ≠ CA² + BA². Donc, le triangle ABC n'est pas rectangle."