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geometry[triangle] - define a triangle
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Calling Sequence
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triangle(T, [A, B, C], n)
triangle(T, [l1, l2, l3], n)
triangle(T, [side1, side2, side3])
triangle(T, [side1, 'angle'=theta, side3], n)
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Parameters
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T
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the name of the triangle
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A, B, C
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three points
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l1, l2, l3
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three lines
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side1, side2, side3
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three sides of the triangle
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side1, 'angle'=theta, side3
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side1 and side3 are the two sides of the triangle, and theta is the angle between them
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n
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(optional) list of two names representing the names of the horizontal-axis and vertical-axis respectively
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Description
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A triangle is a polygon having three sides. A vertex of a triangle is a point at which two of the sides meet.
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A triangle T can be defined as follows:
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from three given points A, B, C.
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from three given lines l1, l2, l3.
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from the sides of the triangle.
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from the two sides of the triangle and the angle between them.
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To access the information relating to a triangle T, use the following function calls:
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form(T)
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returns the form of the geometric object (i.e., triangle2d if T is a triangle).
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HorizontalName(T)
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returns the name of the horizontal-axis; or FAIL if the axis is not assigned a name.
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VerticalName(T)
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returns the name of the vertical-axis; or FAIL if the axis is not assigned a name.
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method(T)
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the method to define the triangle T. They are ``points'' if T is defined from three points or three lines. ``sides'' if T is defined from three sides. ``angle'' if T is defined from two sides, and the angle between them.
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DefinedAs(T)
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returns the list of three vertices of T if T is defined from three points or three lines. the list of three sides of T if T is defined from three sides. the list of two sides and an angle in between if T is defined that way.
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detail(T)
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returns a detailed description of the triangle T.
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The command with(geometry,triangle) allows the use of the abbreviated form of this command.
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Examples
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define three points  , and 
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define the triangle  that has  as its vertices
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![triangle(T1, [A, B, C])](/support/helpjp/helpview.aspx?si=5842/file04142/math234.png)
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![[[0, 0], [1, 1], [1, 0]]](/support/helpjp/helpview.aspx?si=5842/file04142/math258.png)
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define three lines  as follows:
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![line(l1, y = 0, [x, y]), line(l2, y = x, [x, y]), line(l3, x+y-2 = 0, [x, y])](/support/helpjp/helpview.aspx?si=5842/file04142/math266.png)
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define the triangle  from three lines  :
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![triangle(T2, [l1, l2, l3])](/support/helpjp/helpview.aspx?si=5842/file04142/math276.png)
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![[[0, 0], [2, 0], [1, 1]]](/support/helpjp/helpview.aspx?si=5842/file04142/math283.png)
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define the triangle  from three sides:
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![triangle(T3, [3, 3, 3])](/support/helpjp/helpview.aspx?si=5842/file04142/math291.png)
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check if  is a equilateral triangle
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define the triangle  from two sides and the angle between them:
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![triangle(T4, [2, 'angle' = (1/2)*Pi, 1])](/support/helpjp/helpview.aspx?si=5842/file04142/math317.png)
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![[2, angle = (1/2)*Pi, 1]](/support/helpjp/helpview.aspx?si=5842/file04142/math331.png)
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See Also
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geometry[altitude], geometry[area], geometry[AreConjugate], geometry[AreSimilar], geometry[bisector], geometry[centroid], geometry[circumcircle], geometry[EulerCircle], geometry[EulerLine], geometry[excircle], geometry[ExternalBisector], geometry[GergonnePoint], geometry[HorizontalName], geometry[incircle], geometry[IsEquilateral], geometry[IsRightTriangle], geometry[medial], geometry[median], geometry[NagelPoint], geometry[objects], geometry[orthocenter], geometry[sides], geometry[SimsonLine], geometry[VerticalName]
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