# 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.

#### Tools for Construction

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.

#### Constructions

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.

#### Conclusion

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.

#### FAQs

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.

### High School Physics

• Alternating Current
• Atoms
• Communication Systems
• Current Electricity
• Dual nature of Radiation and Matter
• Electric Charges and Fields
• Electricity
• Electromagnetic Induction
• Electromagnetic Waves
• Electron Beams and Radioactivity
• Electrons and Photons
• Electrostatic Potential and Capacitance
• Fluid Pressure
• Force and Acceleration
• Force And Laws Of Motion
• Gravitation
• Internal Energy
• Kinetic Theory
• Law of motion
• Light – Reflection And Refraction
• Magnetic Effects Of Electric Current
• Magnetism and Matter
• Management Of Natural Resources
• Mechanical properties of Fluids
• Mechanical properties of Solids
• Motion
• Motion in a plane
• Motion in a straight line
• Moving Charges and Magnetism
• Nuclear Energy
• Nuclei
• Oscillations
• Our Environment
• Paths of Heat
• Physical world
• Ray optics and optical instruments
• Semiconductor Devices
• Semiconductor Electronics: Materials, Devices and Simple Circuits
• Simple Machines
• Sound
• Sources Of Energy
• Specific and Latent Heats
• Spherical Mirrors
• Static Electricity
• Systems of Particles and Rotational motion
• Thermal properties of matter
• Thermodynamics
• Units and Measurement
• Vectors, Scalar Quantities and Elementary Calculus
• Wave Optics
• Waves
• Work, Power and Energy

### High School Chemistry

• Acids, Bases and Salts
• Alcohols, Phenols and Ethers
• Aldehydes, Ketones and Carboxylic Acids
• Aliphatic and Aromatic Hydrocarbons
• Alkyl and Aryl Halides
• Amines
• Analytical Chemistry
• Atomic Structure
• Atoms And Molecules
• Basic concepts of Chemistry
• Biomolecules
• Carbon And Its Compounds
• Carboxylic acids and Acid Derivatives
• Chemical Bonding and Molecular Structures
• Chemical Energetics
• Chemical Equilibria
• Chemical Kinetics
• Chemical Reactions And Equations
• Chemical Reactions and Their Mechanisms
• Chemistry in Everyday Life
• Chemistry of p-Block elements
• Chemistry of Transition and Inner Transition
• Classification of Elements
• Coordination Compounds
• Cyanide, Isocyanide, Nitro compounds and Amines
• Electrochemistry
• Electrolysis
• Elements, Compounds and Mixtures
• Environmental Chemistry
• Equilibrium
• Ethers and Carbonyl compounds
• Haloalkanes and Haloarenes
• Hydrocarbons
• Hydrogen
• Ideal solutions
• Introduction to Organic Chemistry
• Ionic equilibria
• Matter
• Matter Around Us
• Matter In Our Surroundings
• Metallurgy
• Metals And Non-Metals
• Mole Concept and Stoichiometry
• Natural Resources
• Organic Chemistry – Basic Principles
• Periodic Classification of Elements
• Physical and Chemical Changes
• Physical and Chemical Properties of Water
• Polymers
• Preparation, Properties and Uses of Compounds
• Principles and Processes of Isolation of Elements
• Redox Reactions
• Relative Molecular Mass and Mole
• States of Matter
• Structure Of The Atom
• Study of Compounds
• Study of Gas Laws
• Study of Representative Elements
• Surface Chemistry
• The d-block and f-block elements
• The Gaseous State
• The p-Block Elements
• The Periodic Table
• The s-Block Elements
• The Solid State
• Thermodynamics

### High School Biology

• Absorption and Movement of Water in Plants
• Adolescent Issues
• Anatomy of Flowering Plants
• Animal Kingdom
• Bacteria and Fungi-Friends and Foe
• Biodiversity and Conservation
• Biofertilizers
• Biological Classification
• Biomedical Engineering
• Biomolecules
• Biotechnology and its Applications
• Biotic Community
• Body Fluids and Circulation
• Breathing and Exchange of Gases
• Cell – Unit of Life
• Cell Cycle and Cell Division
• Cell Division and Structure of Chromosomes
• Cell Reproduction
• Cellular Respiration
• Chemical Coordination and Integration
• Circulation
• Control And Coordination
• Crop Improvement
• Digestion and Absorption
• Diversity In Living Organisms
• Ecosystem
• Environmental Issues
• Excretory Products and their Elimination
• Flowering Plants
• Genes and Chromosomes
• Health and Diseases
• Health and Its Significance
• Heredity And Evolution
• Heredity and Variation
• How Do Organisms Reproduce?
• Human Diseases
• Human Eye And Colourful World
• Human Health and Disease
• Human Population
• Human Reproduction
• Hygiene
• Improvement In Food Resources
• Integumentary System- Skin
• Kingdom Fungi
• Kingdom Monera
• Kingdom Protista
• Life Processes
• Locomotion and Movement
• Microbes in Human Welfare
• Mineral Nutrition
• Molecular Basis of Inheritance
• Morphology of Flowering Plants
• Neural Control And Coordination
• Nutrition in Human Beings
• Organism and Population
• Photosynthesis
• Photosynthesis in Higher Plants
• Plant Growth and Development
• Plant Kingdom
• Pollination and Fertilization
• Pollution; Sources and its effects
• Principles of Inheritance and Variation
• Reproduction and Development in Angiosperms
• Reproduction in Organisms
• Reproductive Health
• Respiration in Human Beings
• Respiration in Plants
• Respiratory System
• Sexual Reproduction in Flowering Plants
• Strategies for Enhancement in Food Production
• Structural Organisation in Animals
• Structural Organisation of the Cell
• The Endocrine System
• The Fundamental Unit Of Life
• The Living World
• The Nervous System and Sense Organs
• Tissues
• Transpiration
• Transport in Plants

### High School Math

• Algebra – Arithmatic Progressions
• Algebra – Complex Numbers and Quadratic Equations
• Algebra – Linear Inequalities
• Algebra – Pair of Linear Equations in Two Variables
• Algebra – Polynomials
• Algebra – Principle of Mathematical Induction
• Algebra – Quadratic Equations
• Binomial Theorem
• Calculus – Applications of Derivatives
• Calculus – Applications of the Integrals
• Calculus – Continuity and Differentiability
• Calculus – Differential Equations
• Calculus – Integrals
• Geometry – Area
• Geometry – Circles
• Geometry – Conic Sections
• Geometry – Constructions
• Geometry – Introduction to Euclid’s Geometry
• Geometry – Three-dimensional Geometry
• Geometry – Lines and Angles
• Geometry – Quadrilaterals
• Geometry – Straight Lines
• Geometry – Triangles
• Linear Programming
• Matrices and Determinants
• Mensuration – Areas
• Mensuration – Surface Areas and Volumes
• Number Systems
• Number Systems – Real Numbers
• Permutations and Combinations
• Probability
• Sequence and Series
• Sets and Functions
• Statistics
• Trignometry – Height and Distance
• Trignometry – Identities
• Trignometry – Introduction

### Middle School Science

• Acids, Bases And Salts
• Air and Its Constituents
• Basic Biology
• Body Movements
• Carbon and Its Compounds
• Cell – Structure And Functions
• Changes Around Us
• Chemical Effects Of Electric Current
• Chemistry in Your Life
• Coal And Petroleum
• Combustion And Flame
• Components Of Food
• Conservation Of Plants And Animals
• Crop Production And Management
• Electric Current And Its Effects
• Electricity And Circuits
• Elements and Compounds
• Fibre To Fabric
• Food production and management
• Force And Pressure
• Forests: Our Lifeline
• Friction
• Fun With Magnets
• Garbage In, Garbage Out
• Getting To Know Plants
• Health and Hygiene
• Heat
• Hydrogen
• Life Processes: Nutrition in Animals and Plants
• Light, Shadows And Reflections
• Materials: Metals And Non-Metals
• Matter and Its States
• Metals and Non-metals
• Micro Organisms: Friend And Foe
• Motion And Measurement Of Distances
• Motion And Time
• Nutrition In Animals
• Nutrition In Plants
• Organization in Living Things
• Our Environment
• Physical And Chemical Changes
• Pollution and conservation
• Pollution Of Air And Water
• Reaching The Age Of Adolescence
• Reproduction In Animals
• Reproduction In Plants
• Respiration In Organisms
• Rocks and Minerals
• Separation Of Substances
• Simple Machines
• Soil
• Some Natural Phenomena
• Sorting Materials Into Groups
• Sound
• Stars And The Solar System
• Structure of Atom
• Synthetic Fibers And Plastics
• The Living Organisms And Their Surroundings
• Transfer of Heat
• Transformation of Substances
• Transportation In Animals And Plants
• Universe
• Waste-water Story
• Water: A Precious Resource
• Weather, Climate And Adaptations Of Animals To Climate
• Winds, Storms And Cyclones

### Middle School Math

• Addition
• Area and Its Boundary
• Boxes and Sketches
• Data Handling
• Fun With Numbers
• Heavy and Light
• How Many
• Long And Short
• Mapping
• Measurement
• Money
• Multiplication and Factors
• Multiply and Divide
• Numbers
• Parts and Wholes
• Pattern Recognition
• Patterns
• Play With Patterns
• Rupees And Paise
• Shapes And Angles
• Shapes And Designs
• Shapes and Space
• Similarity
• Smart Charts
• Squares
• Subtraction
• Tables And Shares
• Tenths and Hundredths
• Time
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