📐 fun with Triangles

Do you know Triangles? Check yourself 👍
Trianlge PNG
In Geometry, a triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.

If ABC is a triangle, then it is denoted as ∆ABC, where A, B and C are the vertices of the triangle. A triangle is a two-dimensional shape, in Euclidean geometry, which is seen as three non-collinear points in a unique plane.

Properties

Each and every shape in Maths has some properties which distinguish them from each other. Let us discuss here some of the properties of triangles.

  1. A triangle has three sides and three angles.
  2. The sum of the angles of a triangle is always 180 degrees.
  3. The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Similarly, the difference between the lengths of any two sides of a triangle is less than the length of the third side.

Types

On the basis of the length of the sides, triangles are classified into three categories:

  1. Scalene Triangle
  2. Isosceles Triangle
  3. Equilateral Triangle

On the basis of measurement of the angles, triangles are classified into three categories:

  1. Acute Angle Triangle
  2. Right Angle Triangle
  3. Obtuse Angle Triangle

Scalene Triangle

A scalene triangle is a type of triangle, in which all three sides have different side measures. Due to this, the three angles are also different from each other.
Scalene Triangle PNG

Isosceles Triangle

Isosceles Triangle PNG
In an isosceles triangle, two sides have equal length. The two angles opposite to the two equal sides are also equal to each other.

Equilateral Triangle

An equilateral triangle has all three sides equal to each other. Due to this all the internal angles are of equal degrees, i.e. each of the angles is 60°
Equilateral Triangle PNG

Acute Angled Triangle

Acute Angled Triangle PNG
An acute triangle has all of its angles less than 90°.

Right Angled Triangle

In a right triangle, one of the angles is equal to 90° or right angle.
Right Angled Triangle PNG

Obtuse Angled Triangle

Obtuse Angled Triangle PNG
An obtuse triangle has any of its one angles more than 90°.

Perimeter of Triangle

A perimeter of a triangle is defined as the total length of the outer boundary of the triangle. Or we can say, the perimeter of the triangle is equal to the sum of all its three sides. The unit of the perimeter is the same as the unit of sides of the triangle.

If ABC is a triangle, where AB, BC, and AC are the lengths of its sides, then the perimeter of ABC is given by:
Perimeter = AB+BC+AC

Area of a Triangle

The area of a triangle is the region occupied by the triangle in 2d space. The area for different triangles varies from each other depending on their dimensions. We can calculate the area if we know the base length and the height of a triangle. It is measured in square units.

Suppose a triangle with base ‘B’ and height ‘H’ is given to us, then, the area of a triangle is given by-
Formula:

Area of triangle =  Half of Product of Base and Height
Area = 1/2 × Base × Height
Area Triangle PNG

And

In case, if the height of a triangle is not given, we cannot be able to use the above formula to find the area of a triangle.

Therefore, Heron’s formula is used to calculate the area of a triangle, if all the sides lengths are known.

First, we need to calculate the semi perimeter (s).
s = (a+b+c)/2,                     (where a,b,c are the three sides of a triangle)

Now Area is given by; A = √[s(s-a)(s-b)(s-c)]

Thanks to BYJU'S 🙏, for the above information.