Rigid Motions and Triangle Congruence

Author:
cretsins
You can tell two triangles are congruent by using rigid motions to place one triangle on top of the other. However, there is an easier way to look at two triangles and tell they are congruent if you are given certain angles and side lengths of both triangles. This activity will help us discover which combinations guarantee they are congruent, and which do not.
Let's test out these different sets of equal sides and angles. 1. First, let's set equal side, then adjacent angle, then adjacent side (Side-Angle-Side: SAS). Is there a way to reflect triangle ABC to fit over DEF? What do you notice is true when this combination of angles and sides is true? 2. How about for angle, side, angle? (ASA) 3. What about side, angle, angle? (SAA) 4. What about angle, angle, angle (AAA) and side, side, side (SSS)? CONCLUSION: After this activity what three forms of congruent sides/angles forces the two triangles to be congruent? Which do not?