TAXICAB GEOMETRY
by
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!
