Implement the Triangle class as follows:

 Triangle(PointA, PointB, PointC) instantiates the Triangle object, where Point# is of the given Point class. In each input, two triangles are given.

• Each triangle contents three vertices.
• Triangle.area() returns the area of the Triangle as a float. The following formula to compute the area may be used:
  • | [x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2)]/2 |
  • (x1, y1), (x2, y2), (x3, y3) are 3 vertices of a triangle; | ... | is the absolute function.
  • Return float.
• Triangle.is_triangle() returns whether or not the 3 Points form a valid triangle with a tolerance of TOL, which is given in the file.
  • Return True if it is a valid triangle; False otherwise. (boolean)
• "triangleA == triangleB" compares whether the two triangles are equal. Use Side-Side-Side (SSS) congruence check.
  • SSS congruence states that two Triangles are congruent if every side of one Triangle is of equal length to a corresponding side of another Triangle.
  • For example, a triangle of lengths 3, 4, 5 will be congruent to a triangle of lengths 5, 3, 4 but not to a triangle of 5, 5, 5.
  • Return True if the two triangles are equal; False otherwise. (boolean)
• Note: The file read-in and print statements are already completed. Just fill out the Triangle class.
• The output will be as follows.

    print(triangleA.area())

    print(triangleB.area())

    print(triangleA.is_triangle())

    print(triangleB. is_triangle())

    print(triangleA == triangleB)

 

Template for this question:

import sys

import math

 

TOL = 0.01

 

class Point (object):

  # constructor

  def __init__(self, x = 0, y = 0):

 

  # get the distance to another Point object

  def dist (self, other):

 

class Triangle (object):

    # constructor

    def __init__(self, PointA, PointB, PointC):
 

    # check congruence of Triangles with equality

    # returns True or False (bolean)

    def __eq__(self, other):

 

    # returns whether or not the triangle is valid

    # returns True or False (bolean)

    def is_triangle(self):

 

    # return the area of the triangle:

    def area(self):
 

######################################################

# The code below is filled out, DO NOT EDIT. #

######################################################

 

# takes a string of coordinates and changes it to a list of Points

def get_points(coords_str):

    coords = [float(c) for c in coords_str.split(" ")]

    return [Point(c[0], c[1]) for c in zip(*[iter(coords)]*2)]

 

def main():

    # read the two triangles

    pointsA = get_points(sys.stdin.readline().strip())

    pointsB = get_points(sys.stdin.readline().strip())

 

    triangleA = Triangle(pointsA[0], pointsA[1], pointsA[2])

    triangleB = Triangle(pointsB[0], pointsB[1], pointsB[2])

 

    # Print final output

    print(triangleA.area())

    print(triangleB.area())

    print(triangleA.is_triangle())

    print(triangleB.is_triangle())

    print(triangleA == triangleB)

 

if __name__ == "__main__":

    main()