数学原理：
1、三角形的两边的和一定大于第三边 ,由此亦可证明得三角形的两边的差一定小于第三边.
2、c为最大值边，直角三角形：a^2+b^2=c^2 、钝角三角形：a^2+b^2<c^2 、锐角三角形：a^2+b^2>c^2
程序实现：
Triangle类：用于绘制三角形
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Drawing;
namespace WindowsFormsApplication1
{
class Triangle
{
PointF A, B, C;
public Triangle(PointF a, PointF b, PointF c)
{
A = a;
B = b;
C = c;
}
/// <summary>
/// 绘制三角形
/// </summary>
/// <param name="g"></param>
public void Draw(Graphics g)
{
Pen pen = new Pen(Color.Red, 1);
g.DrawLine(pen, A, B);
g.DrawLine(pen, B, C);
g.DrawLine(pen, C, A);
}
/// <summary>
/// 三角形旋转
/// </summary>
/// <param name="degrees"></param>
public void Rotate(int degrees)
{
float angle = (float)(degrees / 360f * Math.PI);
float newX = (float)(A.X * Math.Cos(angle) - A.Y * Math.Sin(angle));
float newY = (float)(A.X * Math.Sin(angle) + A.Y * Math.Cos(angle));
A.X = newX;
A.Y = newY;
newX = (float)(B.X * Math.Cos(angle) - B.Y * Math.Sin(angle));
newY = (float)(B.X * Math.Sin(angle) + B.Y * Math.Cos(angle));
B.X = newX;
B.Y = newY;
newX = (float)(C.X * Math.Cos(angle) - C.Y * Math.Sin(angle));
newY = (float)(C.X * Math.Sin(angle) + C.Y * Math.Cos(angle));
C.X = newX;
C.Y = newY;
}
}
}
point类：定义坐标点的X，Y
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
namespace WindowsFormsApplication1
{
public class point
{
public double x, y;
public point()
{
;
}
public point(double x, double y)
{
this.x = x;
this.y = y;
}
}
}
judgeTri类：用于判断三角形形状
using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
namespace WindowsFormsApplication1
{
public class judgeTri
{
public double a, b, c;
public judgeTri()
{
;
}
public judgeTri(double a, double b, double c)
{
this.a = a;
this.b = b;
this.c = c;
}
//三角形判断
public bool f1()
{
if (a + b > c || a + c > b || b + c > a)
{
return true;
}
else
return false;
}
//判断值是否等边三角形
public bool f2()
{
if (f1() && a == b && b == c && a == c)
return true;
else
return false;
}
//等腰三角形
public bool f3()
{
if (f1())
if (a == b || b == c || a == c)
return true;
else
return false;
else
return false;
}
//直角三角形
public bool f4()
{
double max;
max = Math.Max(a, b);
max = Math.Max(max, c);
if (max == a)
{
if (Math.Pow(max, 2) == Math.Pow(b, 2) + Math.Pow(c, 2))
return true;
else
return false;
}
else if (max == b)
{
if (Math.Pow(max, 2) == Math.Pow(a, 2) + Math.Pow(c, 2))
return true;
else
return false;
}
else if (max == c)
{
if (Math.Pow(max, 2) == Math.Pow(b, 2) + Math.Pow(a, 2))
return true;
else
return false;
}
else
return false;
}
//钝角三角形
public bool f5()
{
double max;
max = Math.Max(a, b);
max = Math.Max(max, c);
if (max == a)
{
if (Math.Pow(max, 2) > Math.Pow(b, 2) + Math.Pow(c, 2))
return true;
else
return false;
}
else if (max == b)
{
if (Math.Pow(max, 2) > Math.Pow(a, 2) + Math.Pow(c, 2))
return true;
else
return false;
}
else if (max == c)
{
if (Math.Pow(max, 2) > Math.Pow(b, 2) + Math.Pow(a, 2))
return true;
else
return false;
}
else
return false;
}
//锐角三角形
public bool f6()
{
double max;
max = Math.Max(a, b);
max = Math.Max(max, c);
if (max == a)
{
if (Math.Pow(max, 2) < Math.Pow(b, 2) + Math.Pow(c, 2))
return true;
else
return false;
}
else if (max == b)
{
if (Math.Pow(max, 2) < Math.Pow(a, 2) + Math.Pow(c, 2))
return true;
else
return false;
}
else if (max == c)
{
if (Math.Pow(max, 2) < Math.Pow(b, 2) + Math.Pow(a, 2))
return true;
else
return false;
}
else
return false;
}
}
}
Form：
using System;
using System.Collections.Generic;
using System.ComponentModel;
using System.Data;
using System.Drawing;
using System.Linq;
using System.Text;
using System.Windows.Forms;
namespace WindowsFormsApplication1
{
public partial class Form1 : Form
{
point A, B, C;
judgeTri tri;
Triangle t;
string sMessage="";
public double angle_A, angle_B, angle_C;
public Form1()
{
InitializeComponent();
}
//求两点距离
public double pointLen(point m, point n)
{
return Math.Abs(Math.Sqrt(Math.Pow(m.x - n.x, 2) + Math.Pow(m.y - n.y, 2)));
}
//已知三点求角度
public double Angle(point cen, point first, point second)
{
const double M_PI = 3.1415926535897;
double ma_x = first.x - cen.x;
double ma_y = first.y - cen.y;
double mb_x = second.x - cen.x;
double mb_y = second.y - cen.y;
double v1 = (ma_x * mb_x) + (ma_y * mb_y);
double ma_val = Math.Sqrt(ma_x * ma_x + ma_y * ma_y);
double mb_val = Math.Sqrt(mb_x * mb_x + mb_y * mb_y);
double cosM = v1 / (ma_val * mb_val);
double angleAMB = Math.Acos(cosM) * 180 / M_PI;
return angleAMB;
}
private void button1_Click(object sender, EventArgs e)
{
sMessage = "";
A = new point(Convert.ToDouble(AX.Text.Trim()),Convert.ToDouble(AY.Text.Trim()));
B = new point( Convert.ToDouble(BX.Text.Trim()),Convert.ToDouble(BY.Text.Trim()));
C = new point(Convert.ToDouble(CX.Text.Trim()),Convert.ToDouble(CY.Text.Trim()));
tri = new judgeTri();
tri.a = pointLen(B, C);
tri.b = pointLen(A, C);
tri.c = pointLen(A, B);
//计算边长
sMessage += "边长：\na=" + tri.a + "\nb=" + tri.b + "\nc=" + tri.c+"\n";
Message.Text = sMessage;
//判断形状
if (tri.f1())
{
sMessage += "三角形\n";
Message.Text = sMessage;
}
if (tri.f2())
{
sMessage += "等边三角形\n";
Message.Text = sMessage;
}
if (tri.f3())
{
sMessage += "等腰三角形\n";
Message.Text = sMessage;
}
if (tri.f4())
{
sMessage += "直角三角形\n";
Message.Text = sMessage;
}
if (tri.f5())
{
sMessage += "钝角三角形\n";
Message.Text = sMessage;
}
if (tri.f6())
{
sMessage += "锐角三角形\n";
Message.Text = sMessage;
}
//计算角度
sMessage += "角度：\n角A="+Angle(A,B,C)+"度\n角B="+Angle(B,A,C)+"度\n角C="+Angle(C,A,B)+"度\n";
Message.Text = sMessage;
//绘制图形
PointF x = new PointF((float)A.x,(float)A.y);
PointF y = new PointF((float)B.x, (float)B.y);
PointF z = new PointF((float)C.x, (float)C.y);
t = new Triangle(x, y, z);
Graphics g = Draw.CreateGraphics();
g.Clear(Draw.BackColor);
g.TranslateTransform(150, 150);
//绘制标注
Graphics f = Draw.CreateGraphics();
Font font = new Font("微软雅黑", 7);
//Point一样，只是值是浮点类型
PointF point = new PointF((float)A.x, (float)A.y);
g.DrawString("A", font, Brushes.Green, point);
point = new PointF((float)B.x, (float)B.y);
g.DrawString("B", font, Brushes.Green, point);
point = new PointF((float)C.x, (float)C.y);
g.DrawString("C", font, Brushes.Green, point);
t.Draw(g);
}
private void button2_Click(object sender, EventArgs e)
{
AX.Text = AY.Text=BX.Text=BY.Text=CX.Text=CY.Text="";
}
private void Form1_Load(object sender, EventArgs e)
{
}
}
}
设计器代码：
namespace WindowsFormsApplication1
{
partial class Form1
{
/// <summary>
/// 必需的设计器变量。
/// </summary>
private System.ComponentModel.IContainer components = null;
/// <summary>
/// 清理所有正在使用的资源。
/// </summary>
/// <param name="disposing">如果应释放托管资源，为 true；否则为 false。</param>
protected override void Dispose(bool disposing)
{
if (disposing && (components != null))
{
components.Dispose();
}
base.Dispose(disposing);
}
#region Windows 窗体设计器生成的代码
/// <summary>
/// 设计器支持所需的方法 - 不要
/// 使用代码编辑器修改此方法的内容。
/// </summary>
private void InitializeComponent()
{
this.label1 = new System.Windows.Forms.Label();
this.label2 = new System.Windows.Forms.Label();
this.label3 = new System.Windows.Forms.Label();
this.label4 = new System.Windows.Forms.Label();
this.label5 = new System.Windows.Forms.Label();
this.AX = new System.Windows.Forms.TextBox();
this.AY = new System.Windows.Forms.TextBox();
this.BX = new System.Windows.Forms.TextBox();
this.BY = new System.Windows.Forms.TextBox();
this.CX = new System.Windows.Forms.TextBox();
this.CY = new System.Windows.Forms.TextBox();
this.button1 = new System.Windows.Forms.Button();
this.button2 = new System.Windows.Forms.Button();
this.groupBox1 = new System.Windows.Forms.GroupBox();
this.groupBox2 = new System.Windows.Forms.GroupBox();
this.groupBox3 = new System.Windows.Forms.GroupBox();
this.Draw = new System.Windows.Forms.Panel();
this.Message = new System.Windows.Forms.RichTextBox();
this.groupBox1.SuspendLayout();
this.groupBox2.SuspendLayout();
this.groupBox3.SuspendLayout();
this.SuspendLayout();
//
// label1
//
this.label1.AutoSize = true;
this.label1.Location = new System.Drawing.Point(62, 33);
this.label1.Name = "label1";
this.label1.Size = new System.Drawing.Size(11, 12);
this.label1.TabIndex = 1;
this.label1.Text = "X";
//
// label2
//
this.label2.AutoSize = true;
this.label2.Location = new System.Drawing.Point(145, 33);
this.label2.Name = "label2";
this.label2.Size = new System.Drawing.Size(11, 12);
this.label2.TabIndex = 2;
this.label2.Text = "Y";
//
// label3
//
this.label3.AutoSize = true;
this.label3.Location = new System.Drawing.Point(26, 58);
this.label3.Name = "label3";
this.label3.Size = new System.Drawing.Size(23, 12);
this.label3.TabIndex = 3;
this.label3.Text = "点A";
//
// label4
//
this.label4.AutoSize = true;
this.label4.Location = new System.Drawing.Point(26, 86);
this.label4.Name = "label4";
this.label4.Size = new System.Drawing.Size(23, 12);
this.label4.TabIndex = 4;
this.label4.Text = "点B";
//
// label5
//
this.label5.AutoSize = true;
this.label5.Location = new System.Drawing.Point(26, 113);
this.label5.Name = "label5";
this.label5.Size = new System.Drawing.Size(23, 12);
this.label5.TabIndex = 5;
this.label5.Text = "点C";
//
// AX
//
this.AX.Location = new System.Drawing.Point(64, 55);
this.AX.Name = "AX";
this.AX.Size = new System.Drawing.Size(39, 21);
this.AX.TabIndex = 6;
//
// AY
//
this.AY.Location = new System.Drawing.Point(128, 55);
this.AY.Name = "AY";
this.AY.Size = new System.Drawing.Size(39, 21);
this.AY.TabIndex = 7;
//
// BX
//
this.BX.Location = new System.Drawing.Point(64, 83);
this.BX.Name = "BX";
this.BX.Size = new System.Drawing.Size(39, 21);
this.BX.TabIndex = 8;
//
// BY
//
this.BY.Location = new System.Drawing.Point(128, 83);
this.BY.Name = "BY";
this.BY.Size = new System.Drawing.Size(39, 21);
this.BY.TabIndex = 9;
//
// CX
//
this.CX.Location = new System.Drawing.Point(64, 110);
this.CX.Name = "CX";
this.CX.Size = new System.Drawing.Size(39, 21);
this.CX.TabIndex = 10;
//
// CY
//
this.CY.Location = new System.Drawing.Point(128, 110);
this.CY.Name = "CY";
this.CY.Size = new System.Drawing.Size(39, 21);
this.CY.TabIndex = 11;
//
// button1
//
this.button1.Location = new System.Drawing.Point(28, 150);
this.button1.Name = "button1";
this.button1.Size = new System.Drawing.Size(53, 23);
this.button1.TabIndex = 12;
this.button1.Text = "确定(&o)";
this.button1.UseVisualStyleBackColor = true;
this.button1.Click += new System.EventHandler(this.button1_Click);
//
// button2
//
this.button2.Location = new System.Drawing.Point(115, 150);
this.button2.Name = "button2";
this.button2.Size = new System.Drawing.Size(52, 23);
this.button2.TabIndex = 13;
this.button2.Text = "重置";
this.button2.UseVisualStyleBackColor = true;
this.button2.Click += new System.EventHandler(this.button2_Click);
//
// groupBox1
//
this.groupBox1.Controls.Add(this.AX);
this.groupBox1.Controls.Add(this.button2);
this.groupBox1.Controls.Add(this.label1);
this.groupBox1.Controls.Add(this.button1);
this.groupBox1.Controls.Add(this.label2);
this.groupBox1.Controls.Add(this.CY);
this.groupBox1.Controls.Add(this.label3);
this.groupBox1.Controls.Add(this.CX);
this.groupBox1.Controls.Add(this.label4);
this.groupBox1.Controls.Add(this.BY);
this.groupBox1.Controls.Add(this.label5);
this.groupBox1.Controls.Add(this.BX);
this.groupBox1.Controls.Add(this.AY);
this.groupBox1.Location = new System.Drawing.Point(499, 13);
this.groupBox1.Name = "groupBox1";
this.groupBox1.Size = new System.Drawing.Size(200, 212);
this.groupBox1.TabIndex = 15;
this.groupBox1.TabStop = false;
this.groupBox1.Text = "编辑坐标点";
//
// groupBox2
//
this.groupBox2.Controls.Add(this.Message);
this.groupBox2.Location = new System.Drawing.Point(499, 232);
this.groupBox2.Name = "groupBox2";
this.groupBox2.Size = new System.Drawing.Size(200, 229);
this.groupBox2.TabIndex = 16;
this.groupBox2.TabStop = false;
this.groupBox2.Text = "信息展示";
//
// groupBox3
//
this.groupBox3.Controls.Add(this.Draw);
this.groupBox3.Location = new System.Drawing.Point(13, 13);
this.groupBox3.Name = "groupBox3";
this.groupBox3.Size = new System.Drawing.Size(480, 448);
this.groupBox3.TabIndex = 17;
this.groupBox3.TabStop = false;
this.groupBox3.Text = "绘制图形";
//
// Draw
//
this.Draw.Location = new System.Drawing.Point(7, 21);
this.Draw.Name = "Draw";
this.Draw.Size = new System.Drawing.Size(467, 412);
this.Draw.TabIndex = 0;
//
// Message
//
this.Message.Location = new System.Drawing.Point(7, 21);
this.Message.Name = "Message";
this.Message.Size = new System.Drawing.Size(187, 193);
this.Message.TabIndex = 0;
this.Message.Text = "";
//
// Form1
//
this.AutoScaleDimensions = new System.Drawing.SizeF(6F, 12F);
this.AutoScaleMode = System.Windows.Forms.AutoScaleMode.Font;
this.ClientSize = new System.Drawing.Size(788, 517);
this.Controls.Add(this.groupBox3);
this.Controls.Add(this.groupBox2);
this.Controls.Add(this.groupBox1);
this.Name = "Form1";
this.Text = "Form1";
this.Load += new System.EventHandler(this.Form1_Load);
this.groupBox1.ResumeLayout(false);
this.groupBox1.PerformLayout();
this.groupBox2.ResumeLayout(false);
this.groupBox3.ResumeLayout(false);
this.ResumeLayout(false);
}
#endregion
private System.Windows.Forms.Label label1;
private System.Windows.Forms.Label label2;
private System.Windows.Forms.Label label3;
private System.Windows.Forms.Label label4;
private System.Windows.Forms.Label label5;
private System.Windows.Forms.TextBox AX;
private System.Windows.Forms.TextBox AY;
private System.Windows.Forms.TextBox BX;
private System.Windows.Forms.TextBox BY;
private System.Windows.Forms.TextBox CX;
private System.Windows.Forms.TextBox CY;
private System.Windows.Forms.Button button1;
private System.Windows.Forms.Button button2;
private System.Windows.Forms.GroupBox groupBox1;
private System.Windows.Forms.GroupBox groupBox2;
private System.Windows.Forms.GroupBox groupBox3;
private System.Windows.Forms.Panel Draw;
private System.Windows.Forms.RichTextBox Message;
}
}
运行结果：
