Page 1: Calculating Lengths Using Thales' Theorem

This page demonstrates the practical application of Thales' theorem for calcul des longueurs avec Thales. The problem involves calculating lengths FD and FH in a geometric configuration where parallel lines are intersected by secant lines.

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

Example: In the given figure, lines (GH) and (DE) are parallel, intersected by secants at point F. Using the known measurements (FG=4.6, FD=9.2, FE=5.2), we can calculate FH.

Highlight: The key to solving such problems is setting up the correct proportion equation: FG/FH = FD/FE

Vocabulary: Secant lines - lines that intersect at a point

The solution demonstrates how to systematically apply the theorem by writing out the proportions and substituting known values to find the unknown lengths.