Definition: Thales theorem states that if points A, M, B and A, N, C are aligned in the same order and certain proportional relationships exist, then lines (MN) and (BC) are parallel.

Example: Using measurements 4.5, 7.5, and 6 units to verify parallel lines through proportional relationships.

Highlight: The theorem requires careful attention to point alignment and ratio comparisons.

Vocabulary: "Triangle emboîté" - nested triangles, where one triangle is contained within another with parallel corresponding sides.

Definition: In a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides $a² + b² = c²$.

Example: A triangle with sides 4, 5, and 6 units is analyzed to determine if it's right-angled by checking if 16 + 25 = 36.

Highlight: The verification process involves squaring each side length and comparing the sum of squares of two sides with the square of the longest side.

Vocabulary: Hypotenuse - the longest side of a right triangle, opposite to the right angle.