Triangle is a two dimensional figure obtained by joining 3 line segments. It is a polygon with three sides. A triangle has 3 sides, 3 angles and 3 vertices. The symbol used to represent triangle is ?. The below figure represents a triangle.
The triangle is denoted as ?ABC
In the above triangle ABC, A, B and C are the three vertices of the triangle.
AB, BC and AC are the sides of the triangle.
Angle BAC, Angle ABC and Angle ACB are the three angles of the triangle.
Properties of a Triangle
Perimeter: The sum of all the sides of the triangle is called Perimeter.
Sum of the Angles: The sum of all the angles of the triangle is always equal to 180 degrees
Consider the following figure,
In the above figure,
Perimeter P = Side AB + Side BC + Side AC
Sum of the angles, Angle BAC + Angle ABC + Angle ACB = 180 degrees
Area of a triangle:
Area of a triangle is given by the product of 1/2, base and height.
Area = 1/2 * Base * Height
Where any side can be considered as Base
and Height is the perpendicular distance of the base to the opposite vertex
The below diagram explains the area of the triangle.
In the above ?XYZ, YZ is considered as the base. Therefore the perpendicular distance of the base YZ from the opposite vertex X is XM, i.e., XM is the Height of the triangle XYZ
Therefore Area of the ? XYZ = 1/2 * Base * Height
Area = 1/2 * YZ * XM
Area = 1/2 * B * H
Note: Triangle is a two dimensional figure, it does not have volume.
Different Types of Triangles
There are different types of triangles discussed below.
Equilateral Triangles:
Equilateral Triangle is a triangle in which the lengths of all the sides of the triangle are equal. If the sides are equal, then the angles opposite to them will also be equal. Therefore, in an equilateral triangle, all the angles are also equal and equal to 180/3 = 60 degrees.
The figure below shows the diagram of an equilateral triangle.
In the above equilateral triangle, Side AB = Side BC = Side AC
Angle ABC = Angle ACB = Angle BAC = 60 degrees (because sum of all the angles of a triangle is equal to 180 degrees)
Isosceles Triangle:
In an Isosceles triangle, only two of the sides of the triangle are equal. The length of the third side is not equal to the other two sides. Therefore, in any isosceles triangle, two are always equal.
Consider the figure below:
In the above Isosceles triangle XYZ, Side XY = Side XY, and Angle XYZ = Angle XZY
Scalene Triangle:
In a scalene Triangle, all the sides of a triangle are unequal. Therefore no angles in a scalene triangle are equal. The following figure represents a scalene triangle.
In the above scalene triangle MNO, MN ? MO ? ON and
Angle MNO ? Angle MON ? Angle OMN.
Related Tags
Introduction to Triangles, Working on Triangles, Examples for study on Triangles