Isosceles Triangle Theorem

The simple Isosceles Triangle Theorem reflects the power of Euclid’s axiomatic approach in Geometry by providing useful and even profound consequences. Besides illustrating the power of symmetry in enabling useful perfect geometric constructions by ruler and compass, its implications include triangle-circle configurations and tangents to circles; proof of the significant Sum of Three Angles Theorem, and demonstration of the logical equivalences of the Fifth Postulate, Playfair’s Axiom, Sum of Three Angles Proposition, and two other seemingly self-evident propositions. Its another consequence, the Triangle Inequality Theorem offers deep insights into Nature and its processes by highlighting the notion of extremality.