# 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 ` `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; ` `    ``copy = a; ` `    ``copy = b; ` `    ``copy = c; ` `    ``sort(copy, copy + 3); ` `    ``a = copy; ` `    ``b = copy; ` `    ``c = copy; ` `} ` ` `  `// 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
```

## tags:

Geometric triangle Geometric