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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`
PerpendicularFoot
​
PerpendicularFoot
[y,p,u,v]
means that the points
y
,
u
, and
v
are collinear and that the line through points
y
and
p
is perpendicular to the line through points
u
and
v
.
​
Details and Options

Examples  
(2)
Basic Examples  
(1)
Prove that the three altitudes of a triangle are concurrent:
In[1]:=
VerifyConjecture

PerpendicularFoot
[hc,c,a,b],
IsIntersection
hc,c,y,a,b,
IsIntersection
y,ha,a,hb,b,
ECS3
hb,b,c,a,
ECS3
ha,a,b,c,
FreePoint
[a,b,c]
Out[1]=
True
Properties & Relations  
(1)

SeeAlso
Collinear
 
▪
OnPerpendicular
 
▪
PerpendicularLines
 
▪
VerifyConjecture
RelatedGuides
▪
Area Method Proofs
RelatedLinks
▪
The Area Method in the Wolfram Language
- ArXiv article
""

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