Question

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 create a 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 space below.

Answer 1

AAA is not a valid means for establishing congruence. Two triangles with AAA congruence can be similar but not congruent.

An example would be two equilateral triangles, one with side length 1 and one with side length 2.

Both triangles have 3 sides of 60 degrees, but they are not congruent.

Answer 2

Answer with explanation:

AAA -angle-angle-angle, is not a valid criteria for congruence.

This can be explained in the following way.

Consider two equilateral triangles having side measurements , 6 cm, 6 cm, 6 cm and other triangle having side measurements 7 cm, 7 cm and 7 cm.

⇒The two triangles are Similar by Angle -Angle-Angle(AAA) Axiom.It's corresponding sides are proportional and corresponding Angles are equal.

→Similarity, does not imply that the two triangles are congruent.While proving congruency you need to prove the two corresponding sides as well as  corresponding Angles are equal.

⇒To prove the two triangles are congruent,we have to include a side in any of the axioms , which are SAS, SSS, AAS,ASA.

⇒So,we can conclude that , Angle-Angle-Angle (AAA) is a not a valid criterion for establishing triangle congruence.