Triangles

A triangle assignment is a list of 3 variable names followed by the word triangle, right, isosceles or equilateral and some optional parameters. If the first variable is already defined as a point, the triangle is constructed from this point. If not, the point is set to origin. The optional parameter b is the polar angle of segment AB (default: 0°). Here are all the ways to define a triangle when the second variable is not already defined as a point:

• A B C triangle[(x [, b])]
  Defines a scalene triangle with AB = x (default: 6). The triangle is an optimal scalene triangle (i.e. an acute triangle which shape is as far as possible from the shape of right or isosceles triangles).
• A B C triangle(x, y, z [, b])
  Defines a scalene triangle with AB = x, BC = y and AC = z.
• A B C triangle(x, a, a' [, b])
  Defines a scalene triangle with AB = x, measure of the angle under BAC equals a, measure of the angle under CBA equals a'.
• A B C right[(x, y [, a])]
  Defines a right triangle (right angle in A) with AB = x and AC = y (default: 6 and 4.5).
• A B C right(x, a [, b])
  Defines a right triangle (right angle in B) with AB = x and measure of the angle under BAC equals a.
• A B C isosceles[(x, a [, b])]
  Defines an isosceles triangle with AB = x and measure of the angle under BAC and angle under CBA equal a (default: 6 and 39°).
• A B C isosceles(x, y [, b])
  Defines an isosceles triangle with AB = x and AC = BC = y.
• A B C equilateral[(x [, b])]
  Defines an equilateral triangle of side length x (default: 6).

Here are all the ways to define a triangle when the first and the second variables are already defined as points:

• A B C triangle(x, y)
  Defines a scalene triangle with BC = x and AC = y.
• A B C triangle(a, a')
  Defines a scalene triangle with measure of the angle under BAC equals a, measure of the angle under CBA equals a'.
• A B C right(x)
  Defines a right triangle (right angle in A) with AC = x.
• A B C right(a)
  Defines a right triangle (right angle in B) with measure of the angle under BAC equals a.
• A B C isosceles(a)
  Defines an isosceles triangle with measure of the angle under BAC and angle under CBA equal a.
• A B C isosceles(x)
  Defines an isosceles triangle with AC = BC = x.
• A B C equilateral
  Defines an equilateral triangle.