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.  

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

The following figure shows the portion bounded by the three lines.
Triangle Images
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.
Triangle Definition
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.
Triangle Properties
In the above figure $\angle ACD$ = $\angle ABC$ + $\angle BAC$