SAS Exploration Taxicab Geometry

SAS Triangle Condition Exploration in Taxicab Geometry

In this activity we are exploring the SAS Triangle Condition in Taxicab Geometry. Adjust the two lengths for the sides of a triangle and the measure of the included angle by the sliders and/or input boxes. Are there any conditions where there is no triangle possible for the chosen measurements? If so, what conditions do the measurements have to have in order for a triangle to exist? If such a triangle exists, then how many different congruence classes (different sizes of triangles) may result? In Taxicab Geometry, if two triangles exist and they have two corresponding pairs of congruent sides and the corresponding pair of included angles are congruent, do the two triangles have to be congruent? Note that this result is different for Taxicab Geometry than it was in Euclidean Geometry. Given that both Taxicab Geometry and Euclidean Geometry satisfy all the same postulates up to this point, what does this say about the SAS result for Euclidean Geometry?