ASA and AAS Exploration Taxicab Geometry
- Author:
- Dr. Jack L. Jackson II
- Topic:
- Congruence, Geometry, Triangles, Trigonometry
ASA and AAS Conditions in Taxicab Geometry
In this activity we are exploring the ASA (Angle-Side-Angle) and AAS (Angle-Side-Angle) Triangle Conditions in Taxicab Geometry. Subtract the two given angle measures (in radians) from pi to get the measure of the remaining angle. Now we are in the (AASA condition. Adjust the given length of the included side and the measures of the interior angles containing to it 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?
Slowly slide the Step slider to see the construction unfold. If a triangle is possible, how many triangles are produced for a fixed position of A and B? Now move B around the Taxicab circle. What happens to the lengths of the other two sides? For two arbitrary given angle measures and a given side length, how many congruence classes of triangles are possible?
If two triangles exist and they have two corresponding pairs of congruent angles and the corresponding pair of included sides are congruent (ASA Condition), do the two triangles have to be congruent?
If two triangles exist and they have two corresponding pairs of congruent angles and the corresponding pair of sides opposite one of those angle pairs are congruent (AAS Condition), do the two triangles have to be congruent?