Triangles

In this section, we will learn about basic properties of triangles and types of triangles.


Triangle is a closed polygon formed by three intersecting lines. A triangle consists of three sides, three vertices and three angles (As the name suggests “tri angle” means three angles).   

triangle

Here, AB, BC and AC are the sides. 
A, B and C are the three vertices.
∠A , ∠B and ∠C are the three angles.



PROPERTIES OF A TRIANGLE

Following are the basic properties of triangles.

  • The sum of all the three angles of a triangle is always 180º .
  • The sum of any two sides is always greater than the third side.
  • In a triangle, the side opposite to the greater angle is longer.
  • In a triangle, the angle opposite to the longer side is greater.
  • Angles opposite to equal sides of a triangle are equal.
  • Sides opposite to equal angles of a triangle are equal.
  • When a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.
  • The sum of all the sides of a triangle is called its perimeter.Perimeter = sum of all sides = a + b + c
    And half of the perimeter is called semi-perimeter.(s)
    s = ( a + b + c )/ 2
  • Area of a triangle = \frac{1}{2} x Base x Height
  • By Heron’s Formula, 
    Area of a triangle
    = \sqrt{s(s-a)(s-b)(s-c)}

TYPES OF TRIANLGES

Triangles can be classified on the following basis –

 On the basis of sides
  1. Scalene triangle 
  2. Isosceles triangle
  3. Equilateral triangle
On the basis of angles
  1. Acute angled triangle
  2. Obtuse angled triangle
  3. Right angled triangle

Types of triangles on the basis of sides

There are three types of triangles-
a) Scalene triangle – When in a triangle the length of each side is different from another, it is called scalene triangle.
b) Isosceles triangle – When in a triangle, the length of any two sides are equal, then it is called isosceles triangle. 
c) Equilateral triangle – When in a triangle the length of all sides are equal then it is called equilateral triangle.

Area and perimeter of different triangles can be given by-
area and perimeter of triangles

Types of triangles on the basis of angles

  1.  Acute angled triangle – In a triangle when all the angles are acute angles , then the triangle is called acute angled triangle.
    acute angled triangle
  2. Obtuse angled triangle – In a triangle when one angle is obtuse angle, then the triangle is called obtuse angled triangle.
    obtuse angled triangle
  3. Right angled triangle – When one angle of a triangle is 90º, then the triangle is called right angled triangle.
    right angle triangleIn a right angled triangle the side opposite to the 90º angle is the greatest and is called HYPOTENUSE.
    Also, 
    (BC)^{2} = (AC)^{2} + (AB)^{2}
    This is called the Pythagoras theorem.

    It states that, In a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides.
    i.e.
    (Hypotenuse)^{2} = sum of the squares of the other two sides.

You may also want to learn the following for more clear concepts.

TYPES OF ANGLES