Solving Geometric Triangles

Introduction :

          Triangle is a three-sided polygon. ∆ABC denotes a triangle with vertices A, B, and C. There are several types of triangle based on the length of sides and the interior angles, some of them are equilateral triangle, scalene triangle, isosceles triangle, right triangle, oblique triangles, acute triangle, and obtuse triangle.

 

Types of Geometric Triangle by Length of Sides:

 

  • Solving Equilateral Triangle:
              If all the three sides of the triangle are equal then the triangle is Geometric equilateral triangle. Here, all the three angles are also equal, i.e. 60°.

                                                                      


  • Solving Isosceles Triangle:
              If all the two sides of the triangle are equal then the triangle is geometric isosceles triangle. Here, all the three angles are also equal.

                                                                               

  • Solving Scalene triangle:
    In this case, all the sides and the angles are unequal.

                                                          

  

Types of Geometric Triangle by Interior Angles:

 

  • Solving Right-Angled Triangle:
              If any one of the triangles is 90, then the triangle is geometric right-angled triangle. The longest side in the triangle is hypotenuse. i.e. in ∆ABC, AC is hypotenuse.

                                                                            


              The Pythagorean Theorem states that, the sum of squares of length of two legs is equal to the hypotenuse of the right-angled triangle ABC. i.e. AC2 = AB2 + BC2. E.g. Let us consider the right-angled triangle have the leg values AB = 12 and BC = 16, then the hypotenuse should be AC = 20.
  • Solving Oblique Triangles:
              Geometric Oblique triangle is a type of triangle where any of the interior angle is not equal to 90°. There are two cases under oblique triangle, they are,
              Case 1: Acute Triangle or acute - angled triangle
                                       If all the angles in the triangle is less than 90°, then the triangle is acute-angled triangle.

                                                                           


              Case 2: Obtuse Triangles or obtuse-angled triangles
                                       If any one of the angle in the triangle is more than 90°, then the triangle is said to be obtuse-angled triangle.