# Prove Command

From GeoGebra Manual

- 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, GeoGebra Automated Reasoning Tools: A Tutorial and technical details of the algorithms.