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 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. !! I just write in a box!!

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fluttershyjaide fluttershyjaide

25-05-2022
Mathematics

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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 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. !! I just write in a box!!

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ap8997154 ap8997154 · Answer 1 · 2022-05-26T15:03:10+02:00

A triangle is a fundamental form in geometry. The AAA property can not be used to prove if the triangles are congruent.

What is a triangle?

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry.

The property angle-angle-angle (AAA), is used for similar triangles. It can not be used to prove that two triangles are congruent triangles. Therefore, it is not a valid criterion.

Now, this can be proved using two triangles having the same angle measurement as 60°. The two triangles given below has the same angle measurement although, their sides have different measurement, thus, the two triangles are not equal.

Hence, the AAA property can not be used to prove if the triangles are congruent.

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