This page focuses on how to prouver que deux droites sont parallèles using the reciprocal of Thales' theorem. The problem involves determining whether lines (RS) and (KL) are parallel based on given measurements.

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

Example: Using measurements 4.8 and 10.8, the proof compares ratios ER/EK and ES/EL to establish parallelism.

Highlight: The proof requires verifying both the equality of ratios and the alignment of points in the same order.

Vocabulary: Reciprocal theorem - the reverse application of a mathematical principle

The solution methodically demonstrates how to verify the conditions necessary for parallel lines, emphasizing the importance of both ratio equality and point alignment.

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.