# Explore! Napoleon's Theorem - Defining Hypothesis and Thesis

- Author:
- Simona Riva

A triangle is given. Don't read the theorem statement.
Move points changes accordingly.
Use GeoGebra tools to discover the common properties of points , which don't depend on the position of the vertices

*A*,*B*and*C*and observe how triangle*H*,*G*and*I*, and of triangle*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.