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geometry[triangle] - define a triangle
Calling Sequence
triangle(T, [A, B, C], n)
triangle(T, [l1, l2, l3], n)
triangle(T, [side1, side2, side3])
triangle(T, [side1, 'angle'=theta, side3], n)
Parameters
T
-
the name of the triangle
A, B, C
three points
l1, l2, l3
three lines
side1, side2, side3
three sides of the triangle
side1, 'angle'=theta, side3
side1 and side3 are the two sides of the triangle, and theta is the angle between them
n
(optional) list of two names representing the names of the horizontal-axis and vertical-axis respectively
Description
A triangle is a polygon having three sides. A vertex of a triangle is a point at which two of the sides meet.
A triangle T can be defined as follows:
from three given points A, B, C.
from three given lines l1, l2, l3.
from the sides of the triangle.
from the two sides of the triangle and the angle between them.
To access the information relating to a triangle T, use the following function calls:
form(T)
returns the form of the geometric object (i.e., triangle2d if T is a triangle).
HorizontalName(T)
returns the name of the horizontal-axis; or FAIL if the axis is not assigned a name.
VerticalName(T)
returns the name of the vertical-axis; or FAIL if the axis is not assigned a name.
method(T)
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.
DefinedAs(T)
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.
detail(T)
returns a detailed description of the triangle T.
The command with(geometry,triangle) allows the use of the abbreviated form of this command.
Examples
define three points , and
define the triangle that has as its vertices
define three lines as follows:
define the triangle from three lines :
define the triangle from three sides:
check if is a equilateral triangle
define the triangle from two sides and the angle between them:
See Also
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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