Abstract
In the present paper the generalized Propeller theorem from planar Euclidean geometry is extended to all planar affine Cayley–Klein geometries. Since there are no equilateral triangles in affine Cayley–Klein planes (except for the Euclidean case), there is no direct extension of the Propeller theorem. In order to find the respective non-Euclidean analogues of it, we introduce the notion of Ωk-equilateral triangle. Some properties of such triangles are given, too. Finally, we prove a Propeller theorem related to isocentric triangles in all affine Cayley–Klein planes.
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