Difference between revisions of "Prove Command"
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;Prove[ <Boolean Expression> ]: Returns whether the given boolean expression is true or false in general. | ;Prove[ <Boolean Expression> ]: Returns whether the given boolean expression is true or false in general. |
Revision as of 11:12, 29 July 2015
- 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.