Explore! Napoleon's Theorem - Defining Hypothesis and Thesis

A triangle is given. Don't read the theorem statement. Move points A, B and C and observe how triangle changes accordingly. Use GeoGebra tools to discover the common properties of points H, G and I, and of triangle , which don't depend on the position of the vertices A, B and C of the given triangle. Formulate a conjecture about the possible Hypothesis and Thesis of the theorem that you see in the applet, then show the theorem's Statement, and compare them. Explore the construction and discover the Fermat's circles of the sides of the triangle.