AAS Triangle Congruence Exploration Euclidean Geometry

AAS Traingle Congruence Exploration in Euclidean Geometry

In this activity we are exploring the AAS (Angle-Angle-Side) Triangle Condition. 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? 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?