Table of Contents
Introduction
In this article we are going to study basic ideas of plane geometry.
Let us first understand the meaning of term ‘Geometry’. Geometry is derived from word Geometron where Geo means Earth and Metron means Measurement. So, Geometry is a branch of Maths which deals with shape, size and positions of relative figures.
In plane geometry we study about 2D figures or plane figures which have length and breadth but no thickness. Plane figures are drawn on flat surface like on a paper. Examples of 2D figures are circle, triangle, rectangle.
Solid geometry includes study of 3D objects which have length, breadth, height. Examples of these objects are cubes and spheres.
Point, Line Segment, Line, Ray
In this section we frame a definition for point, line segment, line and ray
Point
Let us define a ‘point’.
Suppose we take a pencil and mark a dot on a paper. That dot is simply a point. But how do we define it. Does it have length, breadth and height?
A point is defined as a mark in plane having zero dimensions and it represents a precise location or position.
In the below figure, 3 points are marked, we can denote these points by:
Point A, Point B, Point C
A point can be imagined to be tip of a compass, the sharpened end of a pencil or a pointed end of a needle
Line Segment
The word ‘segment’ means a part of something, in phrase ‘line segment’, it refers to part of a line.
If we take a sheet of paper and fold it and then open it, there will be a crease formed. It has 2 end points, suppose we mark them A and B. We can go from A to B by different paths but the shortest path we take, that will be a straight line, forms the line segment denoted by
AB or BAEither we go from A to B or B to A, we denote line segment by
AB or BA as line segment is defined by end points not direction
Line
If the line segment as discussed above is extended in both directions without any end, we get a line.
A line through two points A and B is written as
Any 2 points determine a unique line that passes through both of them
The image below gives a representation of a line
Ray
A ray is a part of line that starts at one point and goes on infinitely or endlessly in one direction.
In below image, starting point is A, ray passes through B and goes on endlessly
So, it is represented by:
→ ABFor a ray, order matters:
→ AB ≠ → BA
because A is the starting point and the ray extends through B.
Imagine a beam of light from a lighthouse, here starting point can be considered a lighthouse and beam of light goes infinitely in one direction
Similarly ray of light from a torch and sun rays are some other examples of ray.
Watch the below video to understand concepts of point, line segment, line, ray.
Solved Figure it Out Questions from NCERT book based on Point, Line Segment, Line, Ray
Watch the below video for solved figure it questions from NCERT book Ganita Prakash for CBSE class 6 Maths:
Introduction to Angles
Angle is the space formed by two rays when they meet at a common point which is called the vertex of the angle. These two rays are called arms of the angle.
In the below figure, the two rays → CA and → CB meet at vertex C.
Rays → CA and → CB are the arms of ∠C. We can also name the angle as ∠BCA or ∠ACB.
The size of the angle is the amount of rotation or turn needed about the vertex to move from first ray to second ray.
Watch the below video to understand the definition of angle: