AAA Exploration
In the given exploration:
1) You will explore the Angle-Angle-Angle (AAA) case. If the three angles of one triangle are congruent to the three angles of another, must the triangles be congruent?
2) All three angles of the triangle on the right are fixed so that they are always congruent to their corresponding angles 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'.
3) Experiment by moving the points around in order to test the theory that Angle-Angle-Angle (AAA) is a criteria for triangle congruence.
Answer the following questions on binder paper:
4) Can you find a way to make the two triangles look different?
5) Based on your answer to #4, is AAA a valid "shortcut" for triangle congruence?
Optional:
Do you notice any special relationships between the side lengths of the two triangles?