# Prove Command ##### Command Categories (All commands)

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.

• GeoGebra
• Help
• Partners