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

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