# 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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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
```

This article is contributed by Utkarsh Trivedi. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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