What is a triangle?
If three non-collinear points are joined by a straight line, then the closed figure formed is called a triangle.
In the above figure, the three points A, B and C are not collinear, i.e. do not lie on a same straight line.
The figure formed after the three points are joined by a straight line looks like the above one, a Triangle.
A triangle is a closed figure.
The three straight lines AB, AC and BC are called sides or arms of the triangle. So, a triangle has 3 sides all of which are 3 different straight lines.
A triangle is denoted by the symbol
A triangle formed by three non collinear points A, B and C is denoted as
The three points A, B and C of are called Vertices.
Also, a triangle has three angles, formed at the three vertices A, B and C.
The three angles at the three vertices A, B and C are denoted as
The three sides and three angles of a triangle are called parts or elements of a triangle.
Regions inside and outside of a triangle
There are three regions with respect to a triangle:
Interior of, On and Exterior to a triangle.
Interior of a triangle:
In , point x lies inside the triangle. All of the space within the three sides AB, AC and BC form the interior region of the triangle.
On the triangle:
In , point y lies on the side DF, or the triangle DEF.
Exterior to a triangle:
For, point z lies outside. We say point z is in a region exterior to
Properties of angles in a triangle:
Take a, b and c to denote the three angles at the vertices A, B and C. Then,
a + b + c = 1800.
The angle sum property in a triangle is
2. The Exterior angle is equal to sum of the two opposite interior angles of a triangle
Consider the following triangle ABC.
Extend side BC upto point D.
Then an angle at vertex C is formed. It is angle ACD.
This angle ACD is called exterior angle for triangle ABC.
Let x denote angle ACD.
And let a, b, c denote
From angle sum property
i.e. a + b + c = 1800, so c = 1800 – (a + b)
form a linear pair of angles.
Therefore, c + x = 1800
So, c = 1800 – x
But, c = 1800 – (a + b)
Therefore, 1800 – x = 1800 – (a + b), so that we can write
x = a + b