*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!