SSS Triangle Congruence

Exploration of constructing triangles with given sides.
  1. Can you create a triangle with any given side lengths, or are some combinations impossible? Play with the sliders to find out. Keep a table of which combinations of side lengths work and don't work. Can you find any patterns?
  2. How many different shapes are possible for a given set of side lengths? For instance, if you set the lengths to 3, 4, 5, how many different shapes of triangle can you create? What about 4, 4, 5? What is the largest number of shapes you can create for a given set of side lengths? (You may find it helpful to use the angle tool to measure the angles in the triangles to see if triangles are congruent or not.)
  3. Why will GeoGebra let you move points A and B directly (by clicking on them with the arrow tool and dragging), but not point C?