# Checking if an object in space is an isosceles triangle: is_isosceles

### 14.13.10 Checking if an object in space is an isosceles triangle: is_isosceles

See Section 13.16.6 for checking for isosceles triangles in two-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([2,0,0],[0,0,0],[0,2,0])
  Output:

  2

- Input:

  T:= triangle_isosceles([0,0,0],[2,2,0],[2,2,2])
  is_isosceles(T)

  Output:

  1

- Input:
  is_isosceles([1,1,0],[-1,1,0],[-1,0,0])
  Output:

  0