Symbolic geometry software and proofs

Dynamic Geometry software has facilitated an inductive approach to geometry. The dynamic geometry allows students to discover results for themselves, formulate conjectures and intermediate results, examine special cases, and generate new ideas. The new symbolic geometry software, such as Geometry Expressions allows geometric and algebraic representations to coexist in the same model. Symbolic geometry measurements can be used in formulating purely geometrical proofs and also used as the link between the components of a hybrid geometric/algebraic proof. When proving that the incircle of a Pythagorean triangle has integer radius, the expression for the radius is taken as given by the symbolic geometry system, and further algebraic manipulation performed to prove that it is an integer. Displaying symbolic expressions for the length of the median along with coordinates of the triangle vertices and the foot of the median led to a proof path.