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:

The command with(geometry,triangle) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{geometry}\right)\:$

$\mathrm{point}\left(A\,0\,0\right),\mathrm{point}\left(B\,1\,1\right),\mathrm{point}\left(C\,1\,0\right)\:$

$\mathrm{triangle}\left(\mathrm{T1}\,\left[A\,B\,C\right]\right)$

$\mathrm{T1}$

$\mathrm{type}\left(\mathrm{T1}\,'\mathrm{triangle2d}'\right)$

$\mathrm{true}$

$\mathrm{method}\left(\mathrm{T1}\right)$

$\mathrm{points}$

$\mathrm{map}\left(\mathrm{coordinates}\,\mathrm{DefinedAs}\left(\mathrm{T1}\right)\right)$

$\left[\left[0\,0\right]\,\left[1\,1\right]\,\left[1\,0\right]\right]$

$\mathrm{line}\left(\mathrm{l1}\,y=0\,\left[x\,y\right]\right),\mathrm{line}\left(\mathrm{l2}\,y=x\,\left[x\,y\right]\right),\mathrm{line}\left(\mathrm{l3}\,x+y-2=0\,\left[x\,y\right]\right)\:$

$\mathrm{triangle}\left(\mathrm{T2}\,\left[\mathrm{l1}\,\mathrm{l2}\,\mathrm{l3}\right]\right)\:$

$\mathrm{map}\left(\mathrm{coordinates}\,\mathrm{DefinedAs}\left(\mathrm{T2}\right)\right)$

$\left[\left[0\,0\right]\,\left[2\,0\right]\,\left[1\,1\right]\right]$

$\mathrm{triangle}\left(\mathrm{T3}\,\left[3\,3\,3\right]\right)\:$

$\mathrm{detail}\left(\mathrm{T3}\right)$

$\begin{array}{ll}\text{name of the object}& \mathrm{T3}\\ \text{form of the object}& \mathrm{triangle2d}\\ \text{method to define the triangle}& \mathrm{sides}\\ \text{the three sides of the triangle}& \left[3\,3\,3\right]\end{array}$

$\mathrm{IsEquilateral}\left(\mathrm{T3}\right)$

$\mathrm{true}$

$\mathrm{triangle}\left(\mathrm{T4}\,\left[2\,'\mathrm{angle}'=\frac{\mathrm{\pi }}{2}\,1\right]\right)\:$

$\mathrm{method}\left(\mathrm{T4}\right)$

$\mathrm{angle}$

$\mathrm{DefinedAs}\left(\mathrm{T4}\right)$

$\left[2\,\mathrm{angle}=\frac{\mathrm{\pi }}{2}\,1\right]$

$\mathrm{area}\left(\mathrm{T4}\right)$

$1$