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 figure which are enclosed by three sides, called Triangle.”
Triangle is a plan two dimensional geometric shape. It has only Height and Base.

Characteristics/Properties of Triangle

  • A Triangle has three sides.

        AB, BC and CA

  • Three angle in a Triangle.
    ∠A or ∠CAB
    ∠B or ∠ABC
    ∠C or ∠BCA
  • Triangle interior angle sum are 180 degree.
    ∠A + ∠B + ∠C = 180°
    or
    ∠CAB + ∠ABC + ∠BCA = 180°
  • Triangle exterior angle sum are 360° degree.

     

3

∠PAB + ∠QBC + ∠RCA = 360°

  • 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
(B) On the base of angle measure

(A) On the base of side’s measure there are three type of Triangle.

1. Equilateral Triangle
2. Isosceles Triangle
3. Heterogeneous Triangle or scalene triangle
Now we take Dose of them one by one

1. Equilateral Triangle

A triangle which all three sides are equal, called Equilateral Triangle.
Equilateral%2BTriangle
  • All sides are equal so its all Angles are also equal.
  • Each angle is 60 degree in Equilateral Triangle.

Area of Equilateral Triangle 

Equilateral Triangle

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

where a = side of Equilateral Triangle 

2. Isosceles Triangle

A triangle which two sides are equal and third side is different, called Isosceles Triangle.
Isosceles%2BTriangle
  • It’s two sides are equal so it’s opposite angle also equal.

Area of Isosceles Triangle 

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.

Scalene Triangle or Heterogeneous Triangle

Heron’s Formula = \(\displaystyle \sqrt{{s(s-a)(s-b)(s-c)}}\)

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 \(\displaystyle h=\frac{{2A}}{b}\)

Heterogeneous%2BTriangle
  • It’s all sides are unequal so it’s all angle also unequal.
  • ∆ABC जहाँ AB ≠ BC ≠ CA
(B) On the base of angle measure there are three type of Triangle.
1. Acute Angle Triangle
2. right triangle
3. Obtuse Angle Triangle

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

A Triangle which at least one angle are Right angle, called right triangle.
Right%2BAngle%2BTriangle
  • right triangle’s one angle is 90 degree and other two angle have less than 90 degree.

3. Obtuse Angle Triangle

A Triangle which at least one angle are greater than Right angle, called Obtuse Angle Triangle.
 
Obtuse%2BAngle%2BTriangle
  • 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 = \(\displaystyle \frac{1}{2}\times Base\times Height\)
(When the question has been given Base and Height and should be asked for Area)
  • Area of Equilateral Triangle = \(\displaystyle \frac{{\sqrt{3}}}{4}{{a}^{2}}\)
(When the question has been given Base of Equilateral Triangle and should be asked for Area)
  • Area of Triangle by Heron’s Formula = \(\displaystyle \sqrt{{S(S-a)(S-b)(S-c)}}\)
(When the question has been given all three side and should be asked foe area)
Here ‘S’ mean Semi-dimensional.
 
Semi-dimensional (S) = \(\displaystyle \frac{{a+b+c}}{2}\)
   
(Here a, b, c are all three Side of any Heterogeneous Triangle)
  • 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
If the length of the Base and Length is given in a triangle, then the diagonal of that triangle can be known. Similarly, if any two measurements of the triangle are given, then the third measurement can be known.
(Hypotenuse)2 = (Perpendicular)2 + (Base)2
(Perpendicular)2(Hypotenuse)2 – (Base)2
(Base)2(Hypotenuse)2 – (Perpendicular)2
  • The sum of any two sides of the triangle is greater than the third side
The sum of any two sides of the triangle is always greater than its third arm. This is an important feature of the triangle.

We can understand this through the following example.

Example
AB = 6 cm
BC = 3 cm
CA = 5 cm
AB < BC + CA        6 cm < 8 cm
CA < BC + AB        5 cm < 9 cm
BC < AB + CA        3 cm < 11 cm

Medians and Altitude of Triangle

Medians : The line drawn in the middle from the any side on the front vertex of the Triangle is called the median of Triangle.
  • There are 3 Medians in every Triangle.
  • All three Medians has inside the Triangle.
Median
    here AP = Median (from vertex A to the meddle of side BC)
    BP = CP
 
Altitude : A right angle perpendicular which is drawn by a vertex to it’s front side, is called Altitude of Triangle.
  • There are 3 Altitude in every Triangle.
  • Obtuse angle triangle Altitude outside the triangle.
Altitude
    here AP = Altitude (Altitude create a Right angle on opposite side)
    ∠APB = 90°

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