Program to check similarity of given two triangles

Given four array of 3 numbers each which represents sides and angles of two triangles. The task is to check if two triangles are similar or not. If it is similar, print the theorem by which it is.
Examples:

Input : side1 = [2, 3, 3] angle1 = [80, 60, 40]
        side2 = [4, 6, 6]  angle2 = [40, 60, 80]
Output: Triangles are similar by SSS AA SAS 

Input : side1 = [2, 3, 4] angle1 = [85, 45, 50]
        side2 = [4, 6, 6]  angle2 = [40, 60, 80]
Output: Triangles are not similar

Similar triangles are two or more triangles that have all corresponding angles that are equal and all corresponding sides that are proportionate. It does not matter what direction the triangles are facing. Their size does not matter as long as each side is proportionate. The similarity of triangles can be proved by the following theorems:

Side-Side-Side (SSS) similarity criteria :
If all the sides of a triangle are proportional to the corresponding sides of another triangle then the triangles are said to be similar by the property of Side-Side-Side (SSS).
In a triangle ABC and PQR if, AB/PQ = BC/QR = CA/RP triangles are similar.

Side-Angle-Side (SAS) similarity criteria :
If two sides of the two triangles are proportional and the angle between them is same in both triangle then the triangles are said to be similar by the property of Side-Angle-Side (SAS).
In a triangle ABC and PQR if, AB/PQ = BC/QR and = triangles are similar.

Angle-Angle (AA) similarity criteria :
If all the angles of a triangle are equal to the corresponding angles of another triangle then the triangles are said to be similar by the property of Angle-Angle (AA).
In a triangle ABC and PQR if = and = or, = and = or, = and = then triangles are similar.

Below is the implementation of the above approach:

C++

// C++ program to check similarity between two triangles.
 
#include <bits/stdc++.h>

using namespace std;
 
// Function for AA similarity

int simi_aa(float a1[], float a2[])
{

    sort(a1, a1 + 3);

    sort(a2, a2 + 3);
 
    // Check for AA

    if ((a1[0] == a2[0] && a1[1] == a2[1])

        || (a1[0] == a2[0] && a1[2] == a2[2])

        || (a1[1] == a2[1] && a1[2] == a2[2]))

        return 1;

    else

        return 0;
}
 
// Function for SAS similarity

int simi_sas(float s1[], float s2[], float a1[], float a2[])
{

    sort(a1, a1 + 3);

    sort(a2, a2 + 3);

    sort(s1, s1 + 3);

    sort(s2, s2 + 3);
 
    // Check for SAS
 
    // angle b / w two smallest

    // sides is largest.

    if (s1[0] / s2[0] == s1[1] / s2[1]) {

        // since we take angle

        // b / w the sides.

        if (a1[2] == a2[2])

            return 1;

    }

    if (s1[1] / s2[1] == s1[2] / s2[2]) {

        if (a1[0] == a2[0])

            return 1;

    }

    if (s1[2] / s2[2] == s1[0] / s2[0]) {

        if (a1[1] == a2[1])

            return 1;

    }

    return 0;
}
 
// Function for SSS similarity

int simi_sss(float s1[], float s2[])
{

    sort(s1, s1 + 3);

    sort(s2, s2 + 3);
 
    // Check for SSS

    if (s1[0] / s2[0] == s1[1] / s2[1]

        && s1[1] / s2[1] == s1[2] / s2[2]

        && s1[2] / s2[2] == s1[0] / s2[0])

        return 1;
 
    return 0;
}
 
// Driver Code

int main()
{

    float s1[] = { 2, 3, 3 };

    float s2[] = { 4, 6, 6 };
 
    float a1[] = { 80, 60, 40 };

    float a2[] = { 40, 60, 80 };
 
    // function call for AA similarity

    int aa = simi_aa(a1, a2);
 
    // function call for SSS similarity

    int sss = simi_sss(s1, s2);
 
    // function call for SAS similarity

    int sas = simi_sas(s1, s2, a1, a2);
 
    // Check if triangles are similar or not

    if (aa == 1 || sss == 1 || sas == 1) {

        cout << "Triangles are "

             << "similar by ";

        if (aa == 1)

            cout << "AA ";

        if (sss == 1)

            cout << "SSS ";

        if (sas == 1)

            cout << "SAS ";

    }
 
    else

        cout << "Triangles are "

             << "not similar";

    return 0;
}
 
// This code is contributed by Arnab Kundu
 
// This code is modified by Susobhan Akhuli

Java

// Java program to check
// similarity between
// two triangles.

import java.util.*;

class GFG1 {
 
    // Function for

    // AA similarity

    static int simi_aa(float a1[], float a2[])

    {

        Arrays.sort(a1);

        Arrays.sort(a2);
 
        // Check for AA

        if ((a1[0] == a2[0] && a1[1] == a2[1])

            || (a1[0] == a2[0] && a1[2] == a2[2])

            || (a1[1] == a2[1] && a1[2] == a2[2]))

            return 1;

        else

            return 0;

    }
 
    // Function for

    // SAS similarity

    static int simi_sas(float s1[], float s2[], float a1[],

                        float a2[])

    {

        Arrays.sort(a1);

        Arrays.sort(a2);

        Arrays.sort(s1);

        Arrays.sort(s2);
 
        // Check for SAS
 
        // angle b / w two smallest

        // sides is largest.

        if (s1[0] / s2[0] == s1[1] / s2[1]) {

            // since we take angle

            // b / w the sides.

            if (a1[2] == a2[2])

                return 1;

        }

        if (s1[1] / s2[1] == s1[2] / s2[2]) {

            if (a1[0] == a2[0])

                return 1;

        }

        if (s1[2] / s2[2] == s1[0] / s2[0]) {

            if (a1[1] == a2[1])

                return 1;

        }

        return 0;

    }
 
    // Function for

    // SSS similarity

    static int simi_sss(float s1[], float s2[])

    {

        Arrays.sort(s1);

        Arrays.sort(s2);
 
        // Check for SSS

        if (s1[0] / s2[0] == s1[1] / s2[1]

            && s1[1] / s2[1] == s1[2] / s2[2]

            && s1[2] / s2[2] == s1[0] / s2[0])

            return 1;
 
        return 0;

    }
 
    // Driver Code

    public static void main(String args[])

    {

        float s1[] = { 2, 3, 3 };

        float s2[] = { 4, 6, 6 };
 
        float a1[] = { 80, 60, 40 };

        float a2[] = { 40, 60, 80 };
 
        // function call for

        // AA similarity

        int aa = simi_aa(a1, a2);
 
        // function call for

        // SSS similarity

        int sss = simi_sss(s1, s2);
 
        // function call for

        // SAS similarity

        int sas = simi_sas(s1, s2, a1, a2);
 
        // Check if triangles

        // are similar or not

        if (aa == 1 || sss == 1 || sas == 1) {

            System.out.print("Triangles are "

                             + "similar by ");

            if (aa == 1)

                System.out.print("AA ");

            if (sss == 1)

                System.out.print("SSS ");

            if (sas == 1)

                System.out.print("SAS ");

        }

        else

            System.out.println("Triangles are "

                               + "not similar");

    }
}
 
// This code is contributed by Arnab Kundu
 
// This code is modified by Susobhan Akhuli

Python

# Python program to check
# similarity between two triangles.
 
# Function for AA similarity
 
def simi_aa(a1, a2):

    a1 = [float(i) for i in a1]

    a2 = [float(i) for i in a2]

    a1.sort()

    a2.sort()
 
    # Check for AA

    if ((a1[0] == a2[0] and a1[1] == a2[1]) or (a1[0] == a2[0] and a1[2] == a2[2]) or (a1[1] == a2[1] and a1[2] == a2[2])):

        return 1

    return 0
 
# Function for SAS similarity
 
def simi_sas(s1, s2, a1, a2):
 
    s1 = [float(i) for i in s1]

    s2 = [float(i) for i in s2]

    a1 = [float(i) for i in a1]

    a2 = [float(i) for i in a2]
 
    s1.sort()

    s2.sort()

    a1.sort()

    a2.sort()
 
    # Check for SAS
 
    # angle b / w two smallest sides is largest.

    if s1[0] / s2[0] == s1[1] / s2[1]:
 
        # since we take angle b / w the sides.

        if a1[2] == a2[2]:

            return 1
 
    if s1[1] / s2[1] == s1[2] / s2[2]:

        if a1[0] == a2[0]:

            return 1
 
    if s1[2] / s2[2] == s1[0] / s2[0]:

        if a1[1] == a2[1]:

            return 1
 
    return 0
 
# Function for SSS similarity
 
def simi_sss(s1, s2):
 
    s1 = [float(i) for i in s1]

    s2 = [float(i) for i in s2]

    s1.sort()

    s2.sort()
 
    # Check for SSS

    if(s1[0] / s2[0] == s1[1] / s2[1]

            and s1[1] / s2[1] == s1[2] / s2[2]

            and s1[2] / s2[2] == s1[0] / s2[0]):

        return 1
 
    return 0
 
# Driver Code

s1 = [2, 3, 3]

s2 = [4, 6, 6]
 
a1 = [80, 60, 40]

a2 = [40, 60, 80]
 
# function call for AA similarity

aa = simi_aa(a1, a2)
 
# function call for SSS similarity

sss = simi_sss(s1, s2)
 
# function call for SAS similarity

sas = simi_sas(s1, s2, a1, a2)
 
# Check if triangles are similar or not

if aa or sss or sas:

    print "Triangles are similar by",

    if aa:

        print "AA",

    if sss:

        print "SSS",

    if sas:

        print "SAS"

else:

    print "Triangles are not similar"
 
# This code is modified by Susobhan Akhuli

// C# program to check
// similarity between
// two triangles.
 
using System;
 
class GFG1 {
 
    // Function for

    // AA similarity

    static int simi_aa(float[] a1, float[] a2)

    {

        Array.Sort(a1);

        Array.Sort(a2);
 
        // Check for AA

        if ((a1[0] == a2[0] && a1[1] == a2[1])

            || (a1[0] == a2[0] && a1[2] == a2[2])

            || (a1[1] == a2[1] && a1[2] == a2[2]))

            return 1;

        else

            return 0;

    }
 
    // Function for

    // SAS similarity

    static int simi_sas(float[] s1, float[] s2, float[] a1,

                        float[] a2)

    {

        Array.Sort(a1);

        Array.Sort(a2);

        Array.Sort(s1);

        Array.Sort(s2);
 
        // Check for SAS
 
        // angle b / w two smallest

        // sides is largest.

        if (s1[0] / s2[0] == s1[1] / s2[1]) {

            // since we take angle

            // b / w the sides.

            if (a1[2] == a2[2])

                return 1;

        }

        if (s1[1] / s2[1] == s1[2] / s2[2]) {

            if (a1[0] == a2[0])

                return 1;

        }

        if (s1[2] / s2[2] == s1[0] / s2[0]) {

            if (a1[1] == a2[1])

                return 1;

        }

        return 0;

    }
 
    // Function for

    // SSS similarity

    static int simi_sss(float[] s1, float[] s2)

    {

        Array.Sort(s1);

        Array.Sort(s2);
 
        // Check for SSS

        if (s1[0] / s2[0] == s1[1] / s2[1]

            && s1[1] / s2[1] == s1[2] / s2[2]

            && s1[2] / s2[2] == s1[0] / s2[0])

            return 1;
 
        return 0;

    }
 
    // Driver Code

    public static void Main()

    {

        float[] s1 = { 2, 3, 3 };

        float[] s2 = { 4, 6, 6 };
 
        float[] a1 = { 80, 60, 40 };

        float[] a2 = { 40, 60, 80 };
 
        // function call for

        // AA similarity

        int aa = simi_aa(a1, a2);
 
        // function call for

        // SSS similarity

        int sss = simi_sss(s1, s2);
 
        // function call for

        // SAS similarity

        int sas = simi_sas(s1, s2, a1, a2);
 
        // Check if triangles

        // are similar or not

        if (aa == 1 || sss == 1 || sas == 1) {

            Console.Write("Triangles are "

                          + "similar by ");

            if (aa == 1)

                Console.Write("AA ");

            if (sss == 1)

                Console.Write("SSS ");

            if (sas == 1)

                Console.Write("SAS ");

        }

        else

            Console.WriteLine("Triangles are "

                              + "not similar");

    }
}
 
// This code is contributed by Ryuga
 
// This code is modified by Susobhan Akhuli

PHP

<?php
// PHP program to check similarity between 
// two triangles. 
 
// Function for AA similarity 

function simi_aa($a1, $a2) 
{ 

    sort($a1); 

    sort($a2); 

    // Check for AA 

    if (($a1[0] == $a2[0] && $a1[1] == $a2[1])

         || ($a1[0] == $a2[0] && $a1[2] == $a2[2])

         || ($a1[1] == $a2[1] && $a1[2] == $a2[2])) 

        return 1; 

    else

        return 0; 

} 
 
// Function for SAS similarity 

function simi_sas($s1, $s2, $a1, $a2) 
{ 

    sort($a1); 

    sort($a2); 

    sort($s1); 

    sort($s2); 

    // Check for SAS 

    // angle b / w two smallest 

    // sides is largest. 

    if( $s1[0] / $s2[0] == $s1[1] / $s2[1]) 

    { 

        // since we take angle b / w the sides. 

        if ($a1[2] == $a2[2])     

            return 1; 

    } 

    if ($s1[1] / $s2[1] == $s1[2] / $s2[2]) 

    { 

        if ($a1[0] == $a2[0]) 

            return 1; 

    } 

    if ($s1[2] / $s2[2] == $s1[0] / $s2[0]) 

    { 

        if($a1[1] == $a2[1]) 

            return 1; 

    } 

    return 0; 
} 
 
// Function for SSS similarity 

function simi_sss($s1, $s2) 
{ 

    sort($s1); 

    sort($s2); 

    // Check for SSS 

    if($s1[0] / $s2[0] == $s1[1] / $s2[1] && 

       $s1[1] / $s2[1] == $s1[2] / $s2[2] && 

       $s1[2] / $s2[2] == $s1[0] / $s2[0]) 

        return 1; 

    return 0; 
} 
 
// Driver Code 

$s1 = array(2, 3, 3); 

$s2 = array(4, 6, 6); 

$a1 = array(80, 60, 40); 

$a2 = array(40, 60, 80); 
 
// function call for 
// AA similarity 

$aa = simi_aa($a1, $a2); 
 
// function call for 
// SSS similarity 

$sss = simi_sss($s1, $s2) ; 
 
// function call for 
// SAS similarity 

$sas = simi_sas($s1, $s2, 

                $a1, $a2) ; 
 
// Check if triangles 
// are similar or not 

if($aa == 1 || $sss == 1 || $sas == 1) 
{ 

    echo "Triangles are similar by "; 

    if($aa == 1) echo "AA "; 

    if($sss == 1) echo "SSS "; 

    if($sas == 1) echo "SAS "; 
} 
 
else

    echo "Triangles are not similar"; 
 
// This code is contributed by ajit.
// This code is modified by Susobhan Akhuli
?>

Javascript

<script>

    // Javascript program to check 

    // similarity between 

    // two triangles. 

    // Function for 

    // AA similarity 

    function simi_aa(a1, a2) 

    { 

        a1.sort(function(a, b){return a - b});

        a2.sort(function(a, b){return a - b});
 
        // Check for AA 

        if ((a1[0] == a2[0] && a1[1] == a2[1])

         || (a1[0] == a2[0] && a1[2] == a2[2])

         || (a1[1] == a2[1] && a1[2] == a2[2]))

            return 1; 

        else

            return 0; 
 
    } 
 
    // Function for 

    // SAS similarity 

    function simi_sas(s1, s2, a1, a2) 

    { 

        a1.sort(function(a, b){return a - b});

        a2.sort(function(a, b){return a - b});

        s1.sort(function(a, b){return a - b});

        s2.sort(function(a, b){return a - b});
 
        // Check for SAS 
 
        // angle b / w two smallest 

        // sides is largest. 

        if(s1[0] / s2[0] == s1[1] / s2[1]) 

        { 

            // since we take angle 

            // b / w the sides. 

            if (a1[2] == a2[2])         

                return 1; 

        } 

        if (s1[1] / s2[1] == s1[2] / s2[2]) 

        { 

            if (a1[0] == a2[0]) 

                return 1; 

        } 

        if (s1[2] / s2[2] == s1[0] / s2[0]) 

        { 

            if(a1[1] == a2[1]) 

                return 1; 

        } 

        return 0; 

    } 
 
    // Function for 

    // SSS similarity 

    function simi_sss(s1, s2) 

    { 

        s1.sort(function(a, b){return a - b});

        s2.sort(function(a, b){return a - b}); 
 
        // Check for SSS 

        if(s1[0] / s2[0] == s1[1] / s2[1] && 

        s1[1] / s2[1] == s1[2] / s2[2] && 

        s1[2] / s2[2] == s1[0] / s2[0]) 

            return 1; 
 
        return 0; 

    } 

    let s1 = [2, 3, 3]; 

    let s2 = [4, 6, 6]; 

    let a1 = [80, 60, 40]; 

    let a2 = [40, 60, 80]; 

    // function call for 

    // AA similarity 

    let aa = simi_aa(a1, a2); 

    // function call for 

    // SSS similarity 

    let sss = simi_sss(s1, s2) ; 

    // function call for 

    // SAS similarity 

    let sas = simi_sas(s1, s2, a1, a2) ; 

    // Check if triangles 

    // are similar or not 

    if(aa == 1 || sss == 1 || sas == 1) 

    { 

        document.write("Triangles are " + "similar by "); 

        if(aa == 1) document.write("AA "); 

        if(sss == 1) document.write("SSS "); 

        if(sas == 1) document.write("SAS "); 

    } 

    else

        document.write("Triangles are not similar"); 
 
// This code is contributed by rameshtravel07.
 
// This code is modified by Susobhan Akhuli
</script>