Triangle Definition Type Formula
Triangle Definition Type Formula Triangle right triangle we are start today online class about Triangle on “EteacherG” is free educational website. In previous chapter (lesson) we had read about Rectangle. We read today in chapter about Triangle definition, Type of Triangle and Formula of Triangle and properties of Triangle. Triangle is a 2D geometric plane shape. This is also very important chapter for point of view of examination. So read this lesson carefully. We discuss about different type of triangle like right angle triangle, right triangle, scalene triangle, Equilateral Triangle, Isosceles Triangle and we also read about triangles formula, which are very easily explain by our expert team.
There are many types of triangle and each triangle has different type formulas we study about it in Formula of Triangle and properties of Triangle.
Triangle
Simple Definition of Triangle in Easy Words

A Triangle has three sides.
AB, BC and CA

Three angle in a Triangle.

Triangle interior angle sum are 180 degree.

Triangle exterior angle sum are 360° degree.

There are three vertex in a Triangle.
A, B and C

A Triangle has no diagonal.
Type of Triangle
We divided the triangle on basis of two types of triangle –
(A) On the base of side’s measure there are three type of Triangle.
1. Equilateral Triangle

All sides are equal so its all Angles are also equal.

Each angle is 60 degree in Equilateral Triangle.
Area of Equilateral Triangle
Area = \(\displaystyle \frac{{\sqrt{3}}}{4}{{a}^{2}}\)
where a = side of Equilateral Triangle
2. Isosceles Triangle

It’s two sides are equal so it’s opposite angle also equal.
Area of Isosceles Triangle
Area of Triangle Area of Isosceles Triangle \(\displaystyle =\frac{1}{2}\times b\times h\)
3. Scalene Triangle or Heterogeneous Triangle
A triangle which all three sides are not equal, called scalene triangle.
Scalene Triangle Features
 Scalene Triangle has 3 sides but all three sides are unequal.
 There are 3 Angles in Scalene Triangle all angle also unequal.
 perimeter of Scalene Triangle is sum of all three sides.
 formula of Scalene Triangle Area is find by Heron’s formula.
Heron’s Formula = \(\displaystyle \sqrt{{s(sa)(sb)(sc)}}\)
where a, b and c are the sides of a Scalene Triangle
and s = semi perimeter
\(\displaystyle s=\frac{{a+b+c}}{2}\)
Area of Scalene Triangle if b = base and h = height are given –
Area of Scalene Triangle \(\displaystyle =\frac{1}{2}\times b\times h\)
Height of Scalene Triangle if A = Area and b = Base are given –
Height of Scalene Triangle \(\displaystyle h=\frac{{2A}}{b}\)

It’s all sides are unequal so it’s all angle also unequal.
 ∆ABC जहाँ AB ≠ BC ≠ CA
Now we take Dose of them one by one
1. Acute Angle Triangle
A Triangle which all three angle are smaller than Right angle, called Acute Angle Triangle.
 Each angle is less than 90 degree.
2. right triangle

right triangle’s one angle is 90 degree and other two angle have less than 90 degree.
3. Obtuse Angle Triangle

Obtuse Angle Triangle one angle is greater than 90 degree and other two angle are less than 90 degree.
Important Formula Related to Triangle

Area of Triangle = \(\displaystyle \frac{1}{2}\times Base\times Height\)

Area of Equilateral Triangle = \(\displaystyle \frac{{\sqrt{3}}}{4}{{a}^{2}}\)

Area of Triangle by Heron’s Formula = \(\displaystyle \sqrt{{S(Sa)(Sb)(Sc)}}\)
 Equilateral Triangle which has ‘a’ Side it’s Radius of the intersection (r) = \(\displaystyle \frac{a}{{2\sqrt{3}}}\)
 Equilateral Triangle which has ‘a’ Side it’s Radius of the circumcircle = \(\displaystyle \frac{a}{{\sqrt{3}}}\)

Finding a diagonal of right angled triangle

The sum of any two sides of the triangle is greater than the third side
We can understand this through the following example.
Medians and Altitude of Triangle

There are 3 Medians in every Triangle.

All three Medians has inside the Triangle.

There are 3 Altitude in every Triangle.

Obtuse angle triangle Altitude outside the triangle.