Is AAA an angle theorem that you can use to prove that two triangles are congruent?Question 11Select one:a.Nob.Yes

1. Break Down the Problem

The question addresses the Angle-Angle-Angle (AAA) criterion for triangle congruence. Specifically, it asks whether AAA can be used to prove that two triangles are congruent.

2. Relevant Concepts

To understand this, we need to review triangle congruence criteria:

• AAA (Angle-Angle-Angle): states that if two triangles have three angles that are equal, then the triangles are similar, but not necessarily congruent. Similar triangles have the same shape but not necessarily the same size.
• Other Congruence Criteria: The three primary criteria for triangle congruence are:
  • SSS (Side-Side-Side)
  • SAS (Side-Angle-Side)
  • ASA (Angle-Side-Angle)
  • AAS (Angle-Angle-Side)

3. Analysis and Detail

If two triangles have all three angles equal, they are similar triangles. However, similar triangles can be of different sizes. Thus, knowing only the angles does not provide sufficient information to conclude that the triangles are congruent, since congruence requires that the size of the triangles be the same.

4. Verify and Summarize

Given this analysis, we conclude that AAA is not a valid criterion for proving that two triangles are congruent.

Final Answer

No, AAA cannot be used to prove that two triangles are congruent; it only proves that the triangles are similar.