anglesideangle

AngleSideAngle (ASA) is a triangle congruence postulate. It states that if two angles of one triangle are congruent to two angles of another triangle and the included side—the side between those two angles—in the first triangle is congruent to the corresponding included side of the second triangle, then the triangles are congruent; that is, all corresponding parts are equal.

Note: The side must be the one between the two known angles; if the side is not included, the ASA criterion does not apply and other criteria such as AAS or SSA must be considered.

Because the sum of angles in a triangle is 180 degrees, knowing two angles fixes the third angle. Coupled with the equality of the included side, the triangles are uniquely determined up to congruence. In many geometrical deductions, ASA is used as a foundational tool alongside others such as SAS and SSS.

Examples: If triangle ABC has angle A = 50°, angle C = 70°, and side AC = 6, and triangle A'B'C' has corresponding angles and side equal, then triangle ABC is congruent to triangle A'B'C'.

Applications: ASA is commonly used in geometric constructions, proofs, and practical surveying to determine unknown lengths or angles when two angles and the included side are known.