Page 2: The Reciprocal Theorem
This page explores the reciprocal of Thales' theorem and its applications in determining parallel lines through proportional relationships.
Definition: The reciprocal theorem states that if the ratios of corresponding segments are equal MH/MA=MR/ME, then the lines are parallel, provided the points are in the correct order.
Example: In triangle ABC, using the reciprocal theorem, when AF/AB = AE/AC withAF=2,AB=3.6,AE=2.2,andAC=3.96, we can conclude that (FE) is parallel to (BC).
Highlight: The equality of ratios is crucial - if the equations are not equal, the lines cannot be parallel.
Quote: "Si les 2 équations ne sont pas égales alors les droites (HR) et (EA) ne sont pas parallèles" (If the two equations are not equal, then lines (HR) and (EA) are not parallel).