# 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). 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- #### 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. 2. Obtuse angled triangle – In a triangle when one angle is obtuse angle, then the triangle is called obtuse angled triangle. 3. Right angled triangle – When one angle of a triangle is 90º, then the triangle is called right angled triangle. In 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