AA(A) Exploration Taxicab Geometry

Exploring the AA and AAA Triangle Conditions in Taxicab Geometry

In this activity we examine the AA and AAA triangle conditions in Taxicab Geometry. Manipulate the sliders and/or input boxes to select the measures of two of the interior angles of the triangle. Note that the text boxes take the angles in radians. What conditions on these two angles will prevent a triangle from being constructed? What conditions on the two angles guarantee that at least one triangle can be constructed? If a triangle is possible, then what can we say about the third angle? Slowly slide the step slider to see the construction unfold. Manipulate the orange points. How many shapes and sizes (congruence classes) for these triangles are possible with these 2 given angle measures? In Taxicab Geometry, if we have two triangles with 3 corresponding pairs of congruent angles, is that enough to conclude that the triangles are congruent? In Euclidean Geometry, the AA condition is not enough to guarantee congruence of triangles, but it is enough to guarantee similarity of triangles. In Taxicab Geometry, is the AA condition sufficient to guarantee similarity of triangles?