Susan Sexton



Foundations of Geometry I Project

University of Georgia

Fall 2006

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!



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