Foundations of Geometry I Project
University of Georgia
Instructor: Clint McCrory
SAS triangle congruency in Taxicab Geometry
The notion of distance is different in Euclidean and taxicab geometry.
This affects how the SAS triangle congruency works in each geometry.
SAS triangle congruency states that if two sides and their included angle of one triangle
are congruent to two sides and their included angle of another triangle
then the two triangles are congruent.
In the Euclidean plane congruent triangles look like:
In the taxicab plane triangles that meet the SAS criteria are not congruent:
Here taxicab AB = taxicab DE, angle B = angle E, and taxicab BC = taxicab EF.
But it is obvious that the triangles are not congruent!