Vocabulary: Parallel lines are denoted with "//" symbol in geometric notation.

Example: The calculation BP/BC = BR/BD = PR/CD demonstrates the application of proportional relationships.

Highlight: The final result shows BR = 3.3 units, obtained through careful application of proportional relationships.

Definition: The reciprocal of Thales' Theorem states that if corresponding segments are proportional, then the lines are parallel.

Example: Using the ratios CA/CD = CB/CE to prove that lines are parallel.

Highlight: The reciprocal theorem provides a powerful tool for proving parallel relationships between lines.

Example: When AD/AB ≠ AC/AD, the lines (ED) and (CB) cannot be parallel.

Highlight: This example shows how unequal ratios can be used to disprove parallel relationships between lines.

Vocabulary: The term "réciproque" refers to the converse or reciprocal form of the theorem.

Definition: Thales' Theorem states that when two lines intersect two parallel lines, the ratios of corresponding segments are equal.

Example: Using the proportion AE/AC = AD/AB = DE/BC to calculate AB = 1.5 cm.

Highlight: The solution process clearly shows how to set up and solve proportional equations using known segment lengths.