Triangle Shape

Triangle is a geometrical shape with three sides, three vertices and three angles.

Example of Triangles

Structure of Triangle

Consider the triangle ABC in the above image.

(01) Line Segment
The triangle is made up of three line segment.
Here the line segments are AB, BC and CA

(02) Vertices
Vertices are the points where two lines meet.
In triangle there are three vertices: A, B and C

(03) Angles
There are three angles in the triangle.
Here the angles are \angle BAC,\ \angle ACB,\ \angle CBA
They are also called as: \angle A,\ \angle B,\ \angle C

(04) Triangle Name & Symbol
The symbol for triangle is \triangle
The above triangle can be named as \triangle ABC, \triangle BAC , \triangle CAB etc.

Conclusion
Hence, the shape of triangle involve 6 elements; Three Sides and Three Angles

Classification of Triangles

On the basis of 6 elements discussed above, triangles are classified into different types.

There are basically two parameters to triangle classification:
(a) on the basis of side lengths
(b) on the basis of angle measurement
(c) on the basis of both angle and side measurement

Triangle Classification of the basis of lengths

Triangle types on the basis of lengths are:
(a) Scalene Triangle
(b) Isosceles Triangle
(c) Equilateral Triangle

(a) Scalene Triangle
Its a triangle in which all the side lengths are different

In the above figure, ABC is a Scalene Triangle.
Note that its all sides are of different length

(b) Isosceles Triangle
Its a triangle in which two sides have equal length

In the above triangle note side AB = AC = 5 cm
Since the two sides are equal, the above triangle is Isosceles Triangle

(c) Equilateral Triangle
Triangle whose all sides are equal are called equilateral Triangle

In the above triangle all the sides, AB = BC = CA = 5 cms
Since all sides are equal, the triangle is Equilateral triangle

Triangle Classification of the basis of Angle Measurement

(a) Acute Angle Triangle
It’s a triangle in which all the three angles are acute angles.

The angle whose measurement is less than 90 degree is an acute angle.
Hence, in this triangle all the angle measurement is less than 90 degree

In the above triangle, observe all the angles are below 90 degree:
\angle A=80\ degree\\ \\ \angle B=52\ degree\\ \\ \angle C=47\ degree

Hence the above figure is acute triangle

(b) Obtuse angle Triangle
A triangle whose one of the angle is obtuse angle is called Obtuse Angle Triangle

The angle whose measurement is greater than 90 degree but less than 180 degree is called Obtuse Angle.

Hence in Obtuse triangle, one of the angle measurement is greater than 90 degree but less than 180 degree

In the above triangle, observe angle B is an Obtuse angle.
Hence the figure is of Obtuse Angle Triangle.

Note: There can be only one obtuse angle in a triangle.
i.e. it’s not possible to have two obtuse angle in any triangle

(c) Right Angle Triangle
A triangle whose one angle is measured exactly 90 degree is called Right Triangle

An angle which measure exactly 90 degree is called right angle.
Hence, the name Right triangle is taken from the angle concept

In the above figure, observe angle B is exactly 90 degree.
Hence the figure is a right angled triangle

Triangle Classification on the basis of Angle and Sides

This classification is not widely used, but still you should have an idea about its existence

(a) Acute Equilateral triangle
Its a triangle whose all angles are acute and side are equal to each other

Observe the above triangle ABC; you will note that:
⟹ All angles are acute angles
⟹ All sides are equal to each other

Hence the triangle is Acute Equilateral Triangle

(b) Right Isosceles Triangle
In this triangle in which one angle is 90 degree and two sides are equal to each other

In the above triangle, note that:
AB = AC
\angle ABC=90\ degree\\

Two sides are equal and one angle is 90 degree, hence the triangle is Right Isosceles Triangle

(c) Obtuse Scalene Triangle
If all sides are different and one angle is obtuse angles then the triangle is known as Obtuse Scalene Triangle

Note the above triangle:
Angle B is an obtuse angle and its all sides are different

Properties of Triangle

(a) In a triangle there are 12 components: 3 Sides, 3 Vertices and 3 Angles

(b) Sum of all angles of triangle is exactly 180 degree

This is one universal property of triangle.
No matter the type of triangle, the sum of angle will always be 180 degrees

Note: If the sum of angle is not 180 degrees than you are measuring the angles wrong!!!
This is one of the most important property of triangle

(c) The sum of two sides of triangle is always greater than the third side

(01) Is it possible to have triangle with sum of all angles equal to 190 degree?

NO!!
The sum of all angles of triangle is always 180 degree

(02) Is triangle a polygon?

Polygon is classified as geometrical figure having more than three sides.
Hence, Triangle is a part of Polygon Family

(03) Is It possible to have triangle whose two angles are exactly 90 degree?

Not Possible
There can be only one 90 degree angle possible in a triangle.

If there are two 90 degree angles, then the sum of angle will be like this:
90 + 90 + third angle > 180

You can see the sum of angle will go beyond 180 degrees