In this unit, you learned about three acceptable criteria for identifying congruent triangles:angle-side-angle (ASA), side-angle-side (SAS), and side-side-side (SSS).Let's examine some criteria other than these combinations and determine why they do or do not work as a means for establishing triangle congruence.To show that a criterion doesn't work, you must find a counterexample in which the criterion fails; that is, show that two or more non congruent triangles can be constructed with the given measurements.You will create some counterexamples using theGeoGebrageometry tool.If you need help, follow theseinstructionsfor using GeoGebra.

Part A

Determine whether side-side-angle (SSA) is a valid means for establishing triangle congruence.In this case, you know the measure of two adjacent sides and the angle opposite to one of them.If SSA is a valid criterion, explain why.If it isn't valid, use GeoGebra to create counterexample demonstrating that it doesn't work and give an explanation.(Hint:Try constructing a triangle where the known angle is opposite to the shortest known side.) If you construct a counterexample, take a screenshot of your work, save it, and insert the image in the answer space.

Part B

Determine whether angle-angle-angle (AAA) is a valid means for establishing triangle congruence.If it is a valid criterion, explain why.If it isn't valid, use GeoGebra to create counterexample demonstrating that it doesn't work and give an explanation.If you construct a counterexample, take a screenshot of your work, save it, and insert the image in the answer space.

Part C

Determine whether side-angle-angle (SAA) is a valid means for establishing triangle congruence.In this case, you know the measure of a side, an adjacent angle, and the angle opposite to the side.If SAA is a valid criterion, explain why.If it isn't valid, use GeoGebra to create counterexample demonstrating that it doesn't work and give an explanation.If you construct a counterexample, take a screenshot of your work, save it, and insert the image in the answer space.