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AreaMethod

Guides

  • Area Method Proofs

Symbols

  • Collinear
  • Concyclic
  • CongruentAngles
  • ECS1
  • ECS2
  • ECS3
  • ECS4
  • ECS5
  • EqualPoints
  • Equidistant
  • FreePoint
  • IsCentroid
  • IsCircumcenter
  • IsIntersection
  • IsMidpoint
  • IsOrthocenter
  • OnLine
  • OnParallel
  • OnPerpendicular
  • ParallelLines
  • PerpendicularFoot
  • PerpendicularLines
  • PythagoreanDifference
  • SignedArea
  • SignedDistance
  • VerifyConjecture
WolframAlphaMath`AreaMethod`
IsCentroid
​
IsCentroid
[i,a,b,c,construction]
declares
i
to be the centroid of the triangle △
abc
in construction.
​
​
IsCentroid
[i,a,b,c]
represents an operator form of
IsCentroid
that can be applied to an expression.
​
Details and Options

Examples  
(1)
Basic Examples  
(1)
Prove that the centroid, orthocenter, and circumcenter of a triangle are collinear:
In[1]:=
VerifyConjecture

Collinear
[x,y,z],
IsCentroid
z,a,b,c,
IsOrthocenter
y,a,b,c,
IsCircumcenter
x,a,b,c,
FreePoint
[a,b,c],"UseAreaCoordinates"True
Out[1]=
True
SeeAlso
IsCircumcenter
 
▪
IsOrthocenter
 
▪
VerifyConjecture
RelatedGuides
▪
Area Method Proofs
RelatedLinks
▪
The Area Method in the Wolfram Language
- ArXiv article
""

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