Angle-angle-side theorem

The angle-angle-side theorem (AAS theorem) is a rule in geometry for proving that two triangles are congruent.[1] Congruent triangles have the same shap

The angle-angle-side theorem (AAS theorem) is a rule in geometry for proving that two triangles are congruent.[1] Congruent triangles have the same shape and size, even if one is turned, flipped, or moved.[1]

The AAS theorem says that if two angles and one non-included side of one triangle are equal to the corresponding two angles and non-included side of another triangle, then the two triangles are congruent.[1] A non-included side is a side that is not between the two angles. The theorem works because the three angles of every triangle always add up to 180 degrees. If two angles are known, the third angle is also known. If the triangles also have one matching non-included side, they must be the same size and shape.[2]

The AAS theorem is one of several rules used to prove triangle congruence. Other common rules are SSS, SAS, ASA, and the HL theorem.[2]

References

  1. ↑ 1.0 1.1 1.2 "2.3: The ASA and AAS Theorems". Mathematics LibreTexts. 2020-01-22.
  2. ↑ 2.0 2.1 "Euclid's Elements, Book I, Proposition 26". mathcs.clarku.edu.

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