AAS Exploration Spherical Geometry
- Author:
- Dr. Jack L. Jackson II
- Topic:
- Congruence, Geometry, Triangles, Trigonometry
Exploring the AAS Triangle Condition in Spherical Geometry
In this activity we are exploring the AAS (Angle-Angle-Side) Triangle Condition in Spherical Geometry. Adjust the measure of the two interior angles of a triangle and the length of the side opposite the first
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?
Be sure that you look at all possible cases. Try some with a small side length and try some with a large side length. Specifically look at when the side has length pi/2.
If two triangles exist and they have two corresponding pairs of congruent angles and the corresponding pair of sides opposite the first angles are congruent,
do the two triangles have to be congruent?