Prove Command

Prove( <Boolean Expression> ): Returns whether the given boolean expression is true or false in general.

Normally, GeoGebra decides whether a boolean expression is true or not by using numerical computations. However, the Prove command uses symbolic methods to determine whether a statement is true or false in general. If GeoGebra cannot determine the answer, the result is undefined.

We define three free points, A=(1,2), B=(3,4), C=(5,6). The command AreCollinear(A,B,C) yields true, since a numerical check is used on the current coordinates of the points. Using Prove(AreCollinear(A,B,C)) you will get false as an answer, since the three points are not collinear in general, i.e. when we change the points.

Let us define a triangle with vertices A, B and C, and define D=MidPoint(B,C), E=MidPoint(A,C), p=Line(A,B), q=Line(D,E). Now both p∥q and Prove(p∥q) yield true, since a midline of a triangle will always be parallel to the appropriate side. See also interactive version of this example.