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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`
ECS3
​
ECS3
[y,p,u,v,construction]
declares
y
to be the foot of the line through
p
perpendicular to the line through
u
and
v
in
construction
.
​
​
ECS3
[y,p,u,v]
represents an operator form of
ECS3
that can be applied to an expression.
​
Details and Options

Examples  
(2)
Basic Examples  
(2)
Construct the perpendicular foot of a vertex of a triangle:
In[1]:=
ECS3
ha,a,b,c,
FreePoint
[a,b,c]
Out[1]=
aECS1,points{},parameters{},order1,bECS1,points{},parameters{},order2,cECS1,points{},parameters{},order3,haECS3,points{a,b,c},parameters{},order4
​
Show that the three altitudes of a triangle have a common point of intersection:
In[1]:=
altitudes=
ECS3
hc,c,a,b,
ECS3
hb,b,c,a,
ECS3
ha,a,b,c,
FreePoint
[a,b,c]
Out[1]=
aECS1,points{},parameters{},order1,bECS1,points{},parameters{},order2,cECS1,points{},parameters{},order3,haECS3,points{a,b,c},parameters{},order4,hbECS3,points{b,c,a},parameters{},order5,hcECS3,points{c,a,b},parameters{},order6
In[2]:=
VerifyConjecture

EqualPoints
[p,q],
IsIntersection
p,a,ha,b,hb,
IsIntersection
[q,a,ha,c,hc,altitudes],"UseAreaCoordinates"True
Out[2]=
True
SeeAlso
ECS1
 
▪
ECS2
 
▪
ECS4
 
▪
ECS5
 
▪
VerifyConjecture
RelatedGuides
▪
Area Method Proofs
RelatedLinks
▪
The Area Method in the Wolfram Language
- ArXiv article
""

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