A Visual Proof of Thales's Intercept Theorem
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Consider an arbitrary triangle with sides , , . Extend to and to to form a second triangle with third side parallel to . Then the lengths of the sides satisfy the relations and hence , , . In other words, the line segments that are created if two intersecting lines are intercepted by a pair of parallels are proportional.[more]
You can drag the two red points.[less]
Contributed by: Paolo Maraner (March 2017)
Open content licensed under CC BY-NC-SA
 A. Ostermann and G. Wanner, Geometry by Its History, New York: Springer, 2012.
"A Visual Proof of Thales's Intercept Theorem"
Wolfram Demonstrations Project
Published: March 16 2017