Prove Command

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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.

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