Construction of triangles by various elements

A triangle can be uniquely constructed (up to congruence) if certain combinations of sides and angles are known. The most common construction cases are:

• SSS (Side-Side-Side): All three sides are given.
• SAS (Side-Angle-Side): Two sides and the included angle are given.
• ASA (Angle-Side-Angle): Two angles and the included side are given.
• AAS (Angle-Angle-Side): Two angles and a non-included side are given.
• RHS (Right angle-Hypotenuse-Side): For right triangles, the hypotenuse and one other side are given.

Important properties

• Not all combinations of elements determine a unique triangle (e.g., SSA can be ambiguous).

• The triangle inequality must be satisfied for SSS constructions.

• Constructions use compass and straightedge, following geometric steps.