检查给定两个三角形的相似性的程序

给定四个由 3 个数字组成的数组，每个数组代表两个三角形的边和角。任务是检查两个三角形是否相似。如果相似，则打印出它所依据的定理。
例子：

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

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

相似三角形是两个或更多的三角形，它们的所有对应角都相等，所有对应边都成比例。三角形面向什么方向并不重要。只要每一边成比例，它们的大小就无关紧要。三角形的相似性可以由以下定理证明：

1. Side-Side-Side (SSS) 相似性标准：
   如果一个三角形的所有边都与另一个三角形的对应边成正比，则根据边-边-边(SSS) 的属性，三角形被称为相似。
   在三角形 ABC 和 PQR 中，如果 AB/PQ = BC/QR = CA/RP 三角形相似。

1. Side-Angle-Side (SAS) 相似性标准：
   如果两个三角形的两条边成比例并且它们之间的角度在两个三角形中相同，那么根据Side-Angle-Side （SAS）的属性，三角形被称为相似。
   在三角形 ABC 和 PQR 中，如果 AB/PQ = BC/QR 并且$\measuredangle ABC$ = $\measuredangle PQR$三角形是相似的。

1. Angle-Angle-Angle (AAA) 相似性标准：
   如果一个三角形的所有角都等于另一个三角形的对应角，那么根据角-角-角（AAA）的性质，三角形被称为相似。
   在三角形 ABC 和 PQR 中，如果$\measuredangle ABC$ = $\measuredangle PQR$ , $\measuredangle BCA$ = $\measuredangle QRP$和$\measuredangle CAB$ = $\measuredangle RPQ$那么三角形是相似的。

下面是上述方法的实现：

C++

// C++ program to check
// similarity between
// two triangles.
#include
using namespace std;
 
//Function for AAA similarity
int simi_aaa(int a1[], int a2[])
{
    sort(a1, a1 + 3);
    sort(a2, a2 + 3);
     
    // Check for AAA
    if (a1[0] == a2[0] &&
        a1[1] == a2[1] &&
        a1[2] == a2[2])
    return 1;
    else
    return 0;
     
}
 
// Function for
// SAS similarity
int simi_sas(int s1[], int s2[],
             int a1[], int 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(int s1[], int 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()
{
    int s1[] = {2, 3, 3};
    int s2[] = {4, 6, 6};
         
    int a1[] = {80, 60, 40};
    int a2[] = {40, 60, 80};
 
    // function call for
    // AAA similarity
    int aaa = simi_aaa(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(aaa == 1 ||
       sss == 1 || sas == 1)
    {
        cout << "Triangles are "
             << "similar by ";
        if(aaa == 1) cout << "AAA ";
        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

Java

// Java program to check
// similarity between
// two triangles.
import java.util.*;
class GFG1
{
     
// Function for
// AAA similarity
static int simi_aaa(int a1[],
                    int a2[])
{
    Arrays.sort(a1);
    Arrays.sort(a2);
     
    // Check for AAA
    if (a1[0] == a2[0] &&
        a1[1] == a2[1] &&
        a1[2] == a2[2])
    return 1;
    else
    return 0;
     
}
 
// Function for
// SAS similarity
static int simi_sas(int s1[], int s2[],
                    int a1[], int 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(int s1[],
                    int 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[])
{
    int s1[] = {2, 3, 3};
    int s2[] = {4, 6, 6};
         
    int a1[] = {80, 60, 40};
    int a2[] = {40, 60, 80};
 
    // function call for
    // AAA similarity
    int aaa = simi_aaa(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(aaa == 1 ||
       sss == 1 || sas == 1)
    {
        System.out.print("Triangles are " +
                         "similar by ");
        if(aaa == 1) System.out.print("AAA ");
        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

Python

# Python program to check
# similarity between two triangles.
 
# Function for AAA similarity
def simi_aaa(a1, a2):            
    a1 = [float(i) for i in a1]
    a2 = [float(i) for i in a2]
    a1.sort()
    a2.sort()
     
    # Check for AAA
    if a1[0] == a2[0] and 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 AAA similarity
aaa = simi_aaa(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 aaa or sss or sas:
    print "Triangles are similar by",
    if aaa: print "AAA",
    if sss: print "SSS",
    if sas: print "SAS"
else: print "Triangles are not similar"

C#

// C# program to check
// similarity between
// two triangles.
 
using System;
 
class GFG1
{
     
// Function for
// AAA similarity
static int simi_aaa(int [] a1,
                    int [] a2)
{
    Array.Sort(a1);
    Array.Sort(a2);
     
    // Check for AAA
    if (a1[0] == a2[0] &&
        a1[1] == a2[1] &&
        a1[2] == a2[2])
    return 1;
    else
    return 0;
     
}
 
// Function for
// SAS similarity
static int simi_sas(int [] s1, int [] s2,
                    int [] a1, int [] 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(int [] s1,
                    int [] 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()
{
    int [] s1 = {2, 3, 3};
    int [] s2 = {4, 6, 6};
         
    int [] a1 = {80, 60, 40};
    int [] a2 = {40, 60, 80};
 
    // function call for
    // AAA similarity
    int aaa = simi_aaa(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(aaa == 1 ||
    sss == 1 || sas == 1)
    {
        Console.Write("Triangles are " +
                        "similar by ");
        if(aaa == 1) Console.Write("AAA ");
        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

Javascript

    // Javascript program to check
    // similarity between
    // two triangles.
     
    // Function for
    // AAA similarity
    function simi_aaa(a1, a2)
    {
        a1.sort(function(a, b){return a - b});
        a2.sort(function(a, b){return a - b});
 
        // Check for AAA
        if (a1[0] == a2[0] &&
            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
    // AAA similarity
    let aaa = simi_aaa(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(aaa == 1 || sss == 1 || sas == 1)
    {
        document.write("Triangles are " + "similar by ");
        if(aaa == 1) document.write("AAA ");
        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.

输出：

Triangles are similar by AAA SSS SAS