Prove Command

Warning:

This GeoGebra command is heavily under construction. Expect to encounter various problems when trying it out. The syntax or the output of this command may be subject to change.

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.

Example:

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.

Example:

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.

Note: See also ProveDetails command, Boolean values and technical details of the algorithms.