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geometry

  

triangle

  

define a triangle

 

Calling Sequence

Parameters

Description

Examples

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

withgeometry:

define three points A0,0,B1,1, and C1,0

pointA,0,0,pointB,1,1,pointC,1,0:

define the triangle T1 that has A,B,C as its vertices

triangleT1,A,B,C

T1

(1)

typeT1,'triangle2d'

true

(2)

methodT1

points

(3)

mapcoordinates,DefinedAsT1

0,0,1,1,1,0

(4)

define three lines l1,l2,l3 as follows:

linel1,y=0,x,y,linel2,y=x,x,y,linel3,x+y2=0,x,y:

define the triangle T2 from three lines l1,l2,l3:

triangleT2,l1,l2,l3:

mapcoordinates,DefinedAsT2

0,0,2,0,1,1

(5)

define the triangle T3 from three sides:

triangleT3,3,3,3:

detailT3

name of the objectT3form of the objecttriangle2dmethod to define the trianglesidesthe three sides of the triangle3,3,3

(6)

check if T3 is a equilateral triangle

IsEquilateralT3

true

(7)

define the triangle T4 from two sides and the angle between them:

triangleT4,2,'angle'=π2,1:

methodT4

angle

(8)

DefinedAsT4

2,angle=12π,1

(9)

areaT4

1

(10)

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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