Chapter 3

Geometry

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

Geometry is a branch of mathematics that originated many years ago. Euclid and Pythagoras are considered as one of the pioneers in establishing the laws of geometry. The geometry that we are studying today is the Euclidean geometry developed by Euclid. The different parts of the geometry are the different shapes and sizes, line and line segments, points, rays, and more. If you see around yourself, you can find many uses of geometry. The bottles, beds, sofas, vehicles, clocks are all made in a fixed shape of geometry. Your body is a perfect symmetrical object that is balanced on both sides equivalently. Hence geometry is a widely used subject that forms a major part of your examination.

Some of the tools that are used in the construction of geometrical shapes are given below.

  • The ruler: A Ruler is a straight solid edge that is horizontal and used to draw simple straight lines. The markings are done on the ruler in centimetres, and you can draw exact length line segments using the rulers.
  • Compass: The Compass is a hinged, two-arm machine used to draw circles and arcs. In one of the hands, a pencil can be fixed while the other hand has a pointed end. The sharp, needle-like point serves as the loci for circle construction.
  • Divider: A Divider is a similar hinged, two-hand device that is used to compare the different arcs and lengths.
  • Set squares: A Set Square is a triangular scale piece used to draw different angles such as 45, 60, and 90 degrees. It is also used to draw parallel lines. This instrument is used in the verification of symmetry and similarity for the given shapes.
  • Protractor: A Protractor is a semi-circular device used to draw hemispheres and circles along with any angle from 0 to 180 degrees. You can also draw angles from 180 to 360 degrees.

How to construct line segments?

A line segment is a fixed-line with two defined endpoints. To draw a line segment, you need a ruler and a pencil. Measure the ruler for the asked length and draw the line.

How to construct circles?

Circles can be constructed using a compass. First, measure the desired length of the radius using the compass. Then, put the needle end on the paper and rotate the pencil around the needle with the fixed angle.

How to construct the perpendiculars?

Perpendiculars can be constructed using a ruler and set-square or a compass. Let’s check the construction process using the ruler and set square. You need to draw a line using the ruler. Then, by using a set square, set one adjacent side of 90 degrees to that line. Now, mark the point at which you want to draw the parallel line. Similarly, mark three points by moving the ruler to left or right on the line. Now, join these three points and extend them to form parallel lines.

How to construct a bisector of the line segment?

You need a compass to construct the bisector of the given line segment. Take the compass and put one hand on the one end of the line segment and make an arch on both the sides of the line segment. Then, placing the compass needle on the other end of the line segment makes another arc on both sides of the line segment where it cuts the previous arcs. Now, join both the intersection points of the two arcs on the two sides of the line segment to get the perpendicular bisector of the line segment.

Geometry is a branch of mathematics that deals with different shapes and figures. You must have observed the different geometric shapes present around us. There are various tools and techniques used to construct the complex geometrical shapes around us that are being used in different industries in different forms.

  1. What is covered under geometry?
    Geometry covers a major portion of maths and deals with shapes, sizes, solid figures, dimensions, and more.
  1. What are some of the tools that are used in geometrical constructions?
    The tools that are used in the geometrical constructions are ruler, compass, protractor, divider, set-squares, and more.
  1. What are the applications of geometry?
    Geometry has many basic to complex applications, including the most basic as the shape and size of the objects that we use. The complex designs of mechanical objects are achieved through the thorough design of geometric objects and combining them. Geometry forms a major section of your maths question paper.
  1. What is the difference between the line and line-segment?
    The major difference between the line and line segment is that the line has no fixed length and can be extended indefinitely, whereas the line segment has a fixed length.
  1. What are the types of objects based on geometry?
    An object can either be 2D or 3D based on the dimensions.
  1. What are some 3D geometrical shapes?
    Some of the 3D objects are sphere, cone, cuboid, cylinder, hemisphere, and more.
    Line segment video library, you can check the various types of geometry, including the Euclidean and non-Euclidean geometry. You can also check the construction process of different shapes in geometry.

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