Two Angles and a Side?
What If You Have ASA?
In this construction, two pairs of corresponding angles are automatically congruent. Adjust the vertices of the "triangle" on the left so that the included sides are also congruent and the segments actually form a triangle. Is it possible to form two NON-congruent triangles here?
What If You Have SAA?
In this construction, one pair of sides and two pairs of angles are automatically congruent. Adjust the vertices of the "triangle" on the left until you actually have a triangle. Is it possible to form two NON-congruent triangles here?
Mapping One Congruent Triangle Onto Another
Once again, you might want to try mapping Triangle ABC to a congruent partner in each of the GeoGebra task windows above. Or to challenge yourself further, can you accomplish the mapping in fewer transformations than when following the recipe?
ONE Last Question!
Now that we have explored potential 1-, 2-, and 3-letter criteria, we are going to stop looking for shortcuts. Why don't we need to consider 4- or 5-letter criteria?