Which theorem establishes proportionality relationships when parallel lines intersect two intersecting lines?

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In its form commonly taught in France, Thales' theorem establishes proportionality relationships when parallel lines intersect two secant lines. In a triangle, a line parallel to one of the sides thus determines a smaller triangle whose corresponding sides are proportional to those of the initial triangle. This property is used to calculate lengths and demonstrate parallelism thanks to its reciprocal. In other traditions, the name Thales also designates the fact that an angle inscribed in a semicircle is right. The old formulation, limited to a vague relationship between a triangle and a circle, did not make it possible to identify the targeted theorem.