Page 1: Thales Theorem and Algebraic Calculations

This page focuses on the application of the Thales theorem, its reciprocal, and introduces algebraic calculations.

Thales Theorem Application

The page demonstrates the use of the Thales theorem in solving geometric problems. It shows how to calculate lengths in similar triangles using proportions.

Example: In one problem, the Thales theorem is used to find BC = 4.5 cm using the proportion AD/AE = DE/EC.

Reciprocal of Thales Theorem

The reciprocal of Thales theorem is also covered, showing how to prove that lines are parallel when certain proportions are equal.

Definition: The reciprocal of Thales theorem states that if three points on one line create proportional segments on two other lines, then these two lines are parallel.

Remarkable Identities

The page introduces remarkable identities, which are crucial for algebraic manipulations.

Vocabulary: Remarkable identities are algebraic formulas that represent the square of a sum, the square of a difference, and the product of a sum and difference.

Example: (a+b)² = a² + 2ab + b²

Algebraic Calculations

The page concludes with an example of expanding algebraic expressions.

Example: 7(x + 6) = 7x + 42