G.CO.8 ASA Exploration
In the given exploration:
1) You will explore the Angle-Side-Angle (ASA) case. If two angles and the included ("in between") side of one triangle are congruent to two angles and the included side of another, must the two triangles be congruent?
2) The length of segment A'B' is fixed so that it always matches the length of AB. Also, the measures of the angles at A' and B' are fixed so that they always match the angles at A and B. You are free to manipulate all the vertices of triangle ABC, and the lengths of the other sides of triangle A'B'C'.
3) Experiment by moving the points around in order to test the theory that Angle-Side-Angle (ASA) is a criteria for triangle congruence.
Can you find a way to make a triangle with A' and B' that looks different from triangle ABC? Explain why or why not.
Based on your answer above, is ASA a valid "shortcut" for triangle congruence? Explain why or why not.