Task 1: Criteria for Congruent Triangles

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 does not work, you must find a counterexample in which the criterion fails; that is, two or more noncongruent triangles can be constructed with the given measurements. You will make any counterexamples using the GeoGebra geometry tool. If you need help, follow these instructions for using GeoGebra.

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 it is a valid criterion, explain why. If it is not valid, use GeoGebra to makea 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, paste a screenshot of your work in the space below.

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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 is not valid, use GeoGebra to make a counterexample demonstrating that it doesn't work and give an explanation. If you construct a counterexample, paste a screenshot of your work in the space below.

response here:

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 it is a valid criterion, explain why. If it is not valid, use GeoGebra to make a counterexample demonstrating that it doesn't work and give an explanation. If you construct a counterexample, paste a screenshot of your work in the space below.