Name:________________________
Date:_________________________
So You Thought You Understood Triangles:
In class, we discovered that the SAS congruence theorem from our dear friend Euclid
does not always hold to be true in Taxicab Geometry. If SAS doesn’t always work, we
must consider the other congruence theorems from Euclidean Geometry. In Taxicab
Geometry, do the following:
1. Find a pair of incongruent triangles for which “ASA” holds. Graph your example of
incongruent triangles below. Using complete sentences, explain why your two triangles
have congruence with ASA, but are also incongruent triangles.
2. Find a pair of incongruent triangles for which “SAA” holds. Graph your example of
incongruent triangles below. Using complete sentences, explain why your two triangles
have congruence with SAA, but are also incongruent triangles.
3. Find a pair of incongruent triangles for which “SSS” holds. Graph your example of
incongruent triangles below. Using complete sentences, explain why your two triangles
have congruence with SSS, but are also incongruent triangles.
4. Find an isosceles triangle whose base angles are not congruent. Graph your example
below. Using complete sentences, explain why your triangle has two congruent sides, but
the base angles are not congruent.
5. Find an equilateral right triangle. Graph your example below. Using complete
sentences, explain why your triangle is an equilateral triangle with a right angle. Is there
any other orientation?
6. Find a triangle with two congruent angles which is not isosceles. Graph your example
below. Using complete sentences, explain why the triangle has two congruent angles but
is not isosceles in Taxicab Geometry.