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Classify a triangle

We are given co-ordinates of a triangle. The task is to classify this triangle on basis of sides and angle.

Examples:

Input  : p1 = (3, 0), p2 = (0, 4), p3 = (4, 7)
Output : Right Angle triangle and Isosceles

Input  :  p1 = (0, 0), p2 = (1, 1), p3 = (1, 2);
Output :  Triangle is obtuse and Scalene



We can solve this problem by first calculating the side length and then classifying on comparing of side lengths. Classification by sides is simple, if all sides are equal, triangle will be equilateral, if any two sides are equal triangle will be Isosceles otherwise it will be Scalene.
Now angle can be classified by Pythagoras theorem, if sum of square of two sides is equal to square of third side, triangle will be right angle, if less triangle will be acute angle else it will be obtuse angle triangle.
Below is written simple code for classification of triangle :

// C/C++ program to classify a given triangle
#include <bits/stdc++.h>
using namespace std;
  
struct point
{
    int x, y;
    point()    {}
    point(int x, int y) : x(x), y(y)    {}
};
  
//  Utility method to return square of x
int square(int x)
{
    return x * x;
}
  
// Utility method to sort a, b, c; after this
// method a <= b <= c
void order(int &a, int &b, int &c)
{
    int copy[3];
    copy[0] = a;
    copy[1] = b;
    copy[2] = c;
    sort(copy, copy + 3);
    a = copy[0];
    b = copy[1];
    c = copy[2];
}
  
// Utility method to return Square of distance
// between two points
int euclidDistSquare(point p1, point p2)
{
    return square(p1.x - p2.x) + square(p1.y - p2.y);
}
  
//  Method to classify side
string getSideClassification(int a, int b, int c)
{
    //  if all sides are equal
    if (a == b && b == c)
        return "Equilateral";
  
    //  if any two sides are equal
    else if (a == b || b == c)
        return "Isosceles";
  
    else
        return "Scalene";
}
  
//  Method to classify angle
string getAngleClassification(int a, int b, int c)
{
    // If addition of sum of square of two side
    // is less, then acute
    if (a + b > c)
        return "acute";
  
    // by pythagoras theorem
    else if (a + b == c)
        return "right";
  
    else
        return "obtuse";
}
  
//  Method to classify triangle by sides and angles
void classifyTriangle(point p1, point p2, point p3)
{  
    // Find squares of distances between points
    int a = euclidDistSquare(p1, p2);
    int b = euclidDistSquare(p1, p3);
    int c = euclidDistSquare(p2, p3);
  
    // Sort all squares of distances in increasing order
    order(a, b, c);
  
    cout << "Triangle is " +
            getAngleClassification(a, b, c) + " and " +
            getSideClassification(a, b, c) << endl;
}
  
// Driver code
int main()
{
    point p1, p2, p3;
    p1 = point(3, 0);
    p2 = point(0, 4);
    p3 = point(4, 7);
    classifyTriangle(p1, p2, p3);
  
    p1 = point(0, 0);
    p2 = point(1, 1);
    p3 = point(1, 2);
    classifyTriangle(p1, p2, p3);
    return 0;
}

Output:

Triangle is right and Isosceles
Triangle is obtuse and Scalene

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



This article is attributed to GeeksforGeeks.org

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