Introduction to Geometry
What is Geometry?
The word ‘geometry’ comes from two Greek words:
- geo – it means ‘earth’
- metron - it means ‘measurement’.
It is a branch of mathematics that deals with the measurement, properties and relationships of various geometrical shapes, such as points, lines, angles, suface (e.g. triangle, circle, polygon) and solids (e.g. cubes, spheres, cones).
Classification of Geometry
It can be broadly classified into two parts:
Plane Geometry: Plane geometry deals with flat two dimensional shapes like line, triangle, square, rectangle and circle etc. These figures can easily be drawn on paper. In the current module, we will discuss only plane geometry.
Solid Geometry: Solid geometry is about three dimensional objects like cube, sphere, cone, prism, etc. We will cover this in another module – Mensuration.
Apart from these, there are a few branches of maths which are either closely related to Geometry, or wherein we apply the concepts of Geometry.
- Height and Distance (here we use concepts of Geometry, as well as Trigonometry)
- Co-ordinate Geometry
Concepts Related to Plane Geometry
In the chapter of Geometry, we will study about the following topics:
- Lines and Angles
What is a Point?
Definition of Point: A figure whose length, breadth and height cannot be measured is called a point. It is infinitesimal. In other words, we can say that it has no dimensions.
Properties of a Point
Infinite number of lines can be drawn through a point.
We can draw only one line through two distinct points.
Any two given points can be joined by a line, i.e. any two given points are always collinear.
Property 3: Collinear Points
Three or more than three points are said to be collinear, only if a line segment can pass through them. Otherwise, they are called non-collinear points.
There is one and only one circle passing through three given non-collinear points. Also, three non-collinear points are always concyclic.
Property 5: Concyclic Points
Four or more than four points are said to be concyclic, only if a circle can pass through them.