When we think of pyramid we remember the conical shape, where the sides are bounded by triangular surfaces. We see some of the arches are triangular in shape. Triangle is a smallest polygon having three sides. It is a plane figure which is closed. We know that any polygon of more than 3 sides can be split into small triangles. We can form new shapes using triangles of same shapes. In this section let us discuss about the area and perimeter of a triangle, classification of triangles according to their sides and angles, properties of triangles and some problems based on properties of triangles.

## Triangle Definition

What are Triangles? Triangles are closed figures bounded by three straight lines.

The following figure shows the portion bounded by the three lines.

The lines, l, m and n intersect at three non-collinear points, A, B and C and form the triangle $\Delta$ ABC.

We can also state that a triangle is formed by joining three non-collinear points in a plane. The line segments joining the non-collinear points are called the sides of the triangle and the three non-collinear points are called the vertices.

In the above figure the Triangle formed is $\Delta$ ABC.
The vertices of the triangle are A, B and C
The sides of the $\Delta$ ABC are, AB, BC and CA.
Area of a Traingle = $\frac{1}{2}$ x Base x Height

Perimeter of Triangle = Sum of all the sides
= AB + BC + CA

Triangle Properties:
1. Sum of all the Angles of a triangle is equal to 180o .
In the above triangle $\angle A$ + $\angle B$ + $\angle C$ = 180o

2. The Exterior angle of a triangle is equal to sum of the interior opposite angles.

In the above figure $\angle ACD$ = $\angle ABC$ + $\angle BAC$