def main():
    # Initialize counter
    answer = 0
    # Get the user to answer yes or no.
    userAnswer = str(input("Would you like to enter three sides to a" + \
                           "triangle? Please answer yes or no:"))
    # Gather side data
    side1 = int(input("Side 1 Size?"))
    side2 = int(input("Side 2 Size?"))
    side3 = int(input("Side 3 Size?"))
    # Calculate side data
    while userAnswer != 'no':
        answer += 1
        if side1 == side2 == side3:
            print("Equilateral triangle")
            break
        elif side1 != side2 != side3:
            print("Not equilateral or isosceles")
            break
        else:
            print("Isosceles triangle")
            break
    print("Processing is complete. You have evaluated", answer, "sets of sides.")
    main()
    print("Processing is complete. You have evaluated", answer, "sets of sides.")


main()

def main():
    # Initialize counter
    answer = 0
    userAnswer= 'yes'
    # Get the user to answer yes or no and
    # calculate side data, if yes. 
    while userAnswer != 'no':
		   answer += 1
		   userAnswer = str(input("Would you like to enter three sides to a " + \
                           "triangle? Please answer yes or no:"))               
		   if userAnswer == 'no':
			   print("Process is complete. You have evaluated", answer, "sets of sides")
			   break  
		   side1 = int(input("Side 1 Size?"))
		   side2 = int(input("Side 2 Size?"))
		   side3 = int(input("Side 3 Size?"))  
		    		  
		   if side1 == side2 == side3:
			   print("Equilateral triangle")
			   break
		   if side1 != side2 != side3:
			   print("Not equilateral or isosceles")
			   break
		   else: 
			   print("Isosceles triangle")
			   break
main()	

def main():
    # Initialize counter
    answer = 0
    userAnswer = None

    while userAnswer != 'no':
        userAnswer = None
        while userAnswer != 'yes' and userAnswer != 'no':
            userAnswer = input("Would you like to enter three sides to a triangle? Please answer yes or no: ")

        if userAnswer == 'no':
            print("\nProcess is complete. You have evaluated", answer, "sets of sides")
        else:
            side1 = int(input("Side 1 Size? "))
            side2 = int(input("Side 2 Size? "))
            side3 = int(input("Side 3 Size? "))

            if side1 == side2 == side3:
                print("Equilateral triangle")
            elif side1 != side2 and side1 != side3:
                print("Not equilateral or isosceles")
            else:
                print("Isosceles triangle")
            answer += 1
    print('\nTotal number of iterations: {}'.format(answer))
main()

Output:
Would you like to enter three sides to a triangle? Please answer yes or no: yes
Side 1 Size? 1
Side 2 Size? 1
Side 3 Size? 1
Equilateral triangle
Would you like to enter three sides to a triangle? Please answer yes or no: yes
Side 1 Size? 1
Side 2 Size? 2
Side 3 Size? 3
Not equilateral or isosceles
Would you like to enter three sides to a triangle? Please answer yes or no: yes
Side 1 Size? 1
Side 2 Size? 2
Side 3 Size? 1
Isosceles triangle
Would you like to enter three sides to a triangle? Please answer yes or no: no
Process is complete. You have evaluated 3 sets of sides

Total number of iterations: 4