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Explanation

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Copyright © 1996-2018 Alexander Bogomolny

This is a generalization of a theorem about three equilateral triangles, but it also admits a further generalization.

In the current form, it states that a configuration of three similar (and similarly oriented) triangles that share a vertex at which all three non corresponding angles meet has an interesting property. Namely, the midpoints of segments that join not paired "free" vertices of the three triangles form a fourth triangle similar to the given three.

In this form, the theorem is equivalent to the Fundamental Theorem of 3-Bar Motion.

Asymmetric Propeller

1. Asymmetric Propeller (An Interactive Gizmo)
2. Asymmetric Propeller: a Generalization
3. A Case of Similarity
4. Napoleon's Propeller
5. Asymmetric Propeller and Napoleon's Theorem
6. Asymmetric Propeller by Plane Tiling
7. The Final Chapter of the Asymmetric Propeller Story
8. Asymmetric Propeller, the XXI Century

|Activities| |Contact| |Front page| |Contents| |Geometry|

Copyright © 1996-2018 Alexander Bogomolny