Isosceles triangles in space: isosceles_triangle

### 13.7.2 Isosceles triangles in space: isosceles_triangle

See section 12.8.2 for isosceles triangles in the plane.

The isosceles_triangle command returns and draws an isosceles triangle. It takes as arguments one of the following:

- Three points, A, B and P.
  The first two points A and B are vertices of the triangle, the third point P determines the plane and orientation of the triangle. The orientation is so that angle BAP is positive, and the equal interior angles of the isosceles triangle are determined by angle ABP.
  Input:
  A := point(0,0,0); B := point(3,3,3); P := point(0,0,3)
  then:
  isosceles_triangle(A,B,P);
  Output:
- Two points, A and B, and a list consisting of a point P and a real number c.
  The points A and B are vertices of the triangle and P determines the plane and orientation of the triangle as above. The number c is the measure of the equal interior angles.
  Input:
  isosceles_triangle(A,B,[P,3*pi/4])
  Output:

isosceles_triangle can take an optional fourth argument, which is a variable which will be assigned to the third vertex of the triangle.
Input:

isosceles_triangle(A,B,[P,3*pi/4],C)

then:

coordinates(C)

Output:

[(-3*sqrt(2) - 3)/2, (-3*sqrt(2) -3)/2,
(-3*sqrt(2) + 6)/2]