A Visual Proof of Thales's Intercept Theorem

Requires a Wolfram Notebook System
Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.
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.
Contributed by: Paolo Maraner (March 2017)
Open content licensed under CC BY-NC-SA
Snapshots
Details
Reference
[1] A. Ostermann and G. Wanner, Geometry by Its History, New York: Springer, 2012.
Permanent Citation
"A Visual Proof of Thales's Intercept Theorem"
http://demonstrations.wolfram.com/AVisualProofOfThalessInterceptTheorem/
Wolfram Demonstrations Project
Published: March 16 2017