In the exploration below, segments A'B' and B'C' are fixed to match the lengths of their corresponding objects, and the angle at point C' is fixed to be congruent to angle BCA, but you are able to manipulate the other sides and angles. Experiment by moving the points around in order to test the theory that Side-Side-Angle is a criteria for triangle congruence. Is it possible to make the second triangle different than the first, or are they always congruent?

In the given exploration, all three angles of the triangle on the right are fixed so that they are always congruent to their corresponding angle in the triangle on the left. You are free to manipulate all the vertices of triangle ABC, as well as the side lengths and position of triangle A'B'C'. [br][br]Can you find a way to make the two triangles look different? [br][br]Do you notice any special relationships between the side lengths of the two triangles?