Library/Geometry/Plane geometry/Constructs/Triangle (constructions)

Triangle (constructions)

Overview
Important

Triangle constructions are geometric procedures to create a triangle with given measurements, typically using only a straightedge and compass. The most common cases are SSS (three sides), SAS (two sides and the included angle), ASA (two angles and the included side), and RHS (right angle, hypotenuse, and one side).

Important properties

  • A triangle is uniquely determined by three suitable pieces of information (not all combinations work).

  • The triangle inequality must be satisfied: the sum of any two sides must be greater than the third.

  • Constructions use basic geometric tools: straightedge and compass.

  • Some combinations (like AAA) do not determine a unique triangle up to congruence.