My solution for http://programmingpraxis.com/2013/01/18/triangle-trilemma/

classify_triangle.py

#!/usr/bin/env python


def is_triangle(a, b, c):
    return not collinear(a, b, c)


def collinear(a, b, c):
    return slope(a, b) == slope(b, c)


def slope(point1, point2):
    """
    Returns the slope of two points, or none if they have the same 'x' value,
    since slope for a vertical line is undefined.
    """
    if point1[0] == point2[0]:
        return None
    else:
        return (point1[1] - point2[1]) / (point1[0] - point2[0])


def square_of_distance(pointA, pointB):
    return (pointA[0] - pointB[0]) ** 2 + (pointA[1] - pointB[1]) ** 2


def get_distances_squared(a, b, c):
    return square_of_distance(a,b), square_of_distance(a,c), square_of_distance(b,c)


def classify_shape(side1, side2, side3):
    distances = set([side1, side2, side3])

    if len(distances) == 1:
        tri_type = "equilateral"
    elif len(distances) == 2:
        tri_type = "isosceles"
    elif len(distances) == 3:
        tri_type = "scalene"
    return tri_type


def classify_angles(side1, side2, side3):
    sides = sorted([side1, side2, side3])
    #Pythagorean theorem, and the other cases
    if (sides[0] + sides[1]) == sides[2]:
        angles_type = "right"
    elif (sides[0] + sides[1]) < sides[2]:
        angles_type = "obtuse"
    else:
        angles_type = "acute"
    return angles_type


def classify_triangle(a, b, c):
    if is_triangle(a, b, c):
        side1, side2, side3 = get_distances_squared(a, b, c)
        shape = classify_shape(side1, side2, side3)
        angles = classify_angles(side1, side2, side3)
        print shape + " -> " + angles
    else:
        print "Not a triangle"


if __name__ == '__main__':
    classify_triangle((0, 0), (0, 4), (1, 2))
    classify_triangle((1, 1), (1, 4), (3, 2))
    classify_triangle((2, 2), (2, 4), (4, 3))
    classify_triangle((3, 3), (3, 4), (5, 3))
    classify_triangle((4, 4), (4, 5), (5, 6))
    classify_triangle((5, 5), (5, 6), (6, 5))
    classify_triangle((6, 6), (6, 7), (6, 8))
    classify_triangle((7, 7), (7, 7), (7, 7))
    #tests:
    classify_triangle((0, 1), (0, 2), (0, 3))
    classify_triangle((0, 0), (1, 5), (2, 0))
    classify_triangle((0, 0), (10, 5), (20, 0))
    classify_triangle((0, 0), (0, 5), (5, 0))
    classify_triangle((0, 0), (10, 5), (20, 1))
    classify_triangle((0, 0), (0, 3), (4, 0))
    classify_triangle((0, 0), (2, 4), (4, 1))
    classify_triangle((0, 0), (1, 1), (2, 2))
    classify_triangle((0, 0), (0, 2), (0, 0))
    classify_triangle((0, 0), (0, 2), (0, 1))