SAS Exploration Hyperbolic Geometry
SAS Exploration in Hyperbolic Geometry
In this activity we are examining the SAS condition in Hyperbolic Geometry.
Adjust the lengths of the two sides and the measure of the included angle via the sliders and/or input boxes.
Slowly slide the step slider one step at a time to see the construction unfold. Experiment by moving the orange points A and B, and experiment with different values for the given measurements.
Is there any condition on the measurements that would make the triangle impossible to construct?
If a triangle exists, how many differently shaped triangles (congruence classes) can we form with a specific set of given measurements?
If two triangles have two pair of corresponding congruent sides, and the corresponding included angles are congruent (SAS Condition), then do the two triangles have to be congruent in Hyperbolic Geometry?