13.16.6  Checking if an object in the plane is an isosceles triangle: is_isosceles

See Section 14.13.10 for checking for isosceles triangles in three-dimensional geometry.

The is_isosceles command determines whether or not a geometric object is an isoceles triangle.

• is_isosceles takes one argument:
  G, a geometric object or a sequence of three points assumed to be the vertices of a triangle.
• is_isosceles(G) returns 1,2 or 3 if the object is an isoceles triangle (the number indicates which vertex is on two equal sides), returns 4 if the object is an equilateral triangle, and returns 0 otherwise.

Examples.

• Input:
  is_isosceles(0, 1+i,i)
  Output:

  2

• Input:

  T:= isosceles_triangle(0,1,pi/4)

  is_isosceles(T)

  Output:

  1

• Input:

  T:= isosceles_triangle(0,1,pi/4,C)

  is_isosceles(T[0])

  Output:

  1

  Note that T[0] is a triangle since T is a list made of a triangle and the vertex C.
  Input:
  affix(C)
  Output:

  √ 2 2

  +

  √ 2 2

  i

• Input:
  is_isosceles(1+i, -1+i, -i)
  Output:

  3

• Input:
  is_isosceles(0,2,1+i*sqrt(3))
  Output:

  4