# Chapter 4 – Geometry

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

Introduction

Have you ever pondered that the various shapes and objects we see in our daily lives are a part of geometry? Indeed, geometry is the branch of mathematics that comprises shapes, angles, dimensions, and sizes of different objects and even represents 3D and 2D figures. Basic geometry is based on points, lines, and planes. To calculate the area, perimeter, and volume of shapes, geometric concepts are widely used. For example, a circle also refers to a geometrical shape made with the help of a curve that always has the same distance.

Understanding shapes, positions, angles, and dimensions of objects is pivotal to solve any geometry-related problem. There are different types of shapes in geometry used in better apprehension of the subject matter. It is also helpful in calculating the area, perimeter, and volume of shapes, like the idea of reflection states a transformation, depicting a flip of a figure. These figures may represent a point, line, or plane.

#### Branches of Geometry

There are five branches of geometry, namely:

• Algebraic geometry: This is one of the branches of geometry that deals with the multivariate, polynomial zeros. Algebraic geometry is based on abstract algebraic methodologies required to solve geometric problems related to zeros. It is applied in phylogenetics, cryptography, string theory, etc. Today, algebraic geometry holds a focal role in modern mathematics.
• Discrete geometry: This is also known as combinatorial geometry. It refers to studying geometrical objects like points, lines, triangles, and circles that are discrete either by their nature or by their exhibition. This topic mainly covers the combinatorial properties of various objects and assists in establishing relationships among them.
• Differential geometry: Differential geometry is a mathematical discipline that employs differential calculus, integral calculus, linear algebra, and multilinear algebra to investigate quandaries in geometry. It was found by Sir Isaac Newton and Leibniz for plane bends in the 17th century and by the Swiss mathematician Leonhard Euler for bends in space in the18th century.
• Euclidean geometry is a prominent branch of mathematics, coined by Alexandrian Greek mathematician Euclid in his book on geometry. Euclid’s technique comprises accepting a little arrangement of instinctively engaging and reasoning numerous recommendations from these. In other words, it represents the axiomatic system where true statements are derived from small axioms.
• Convex geometry: In mathematics, convex geometry refers to convex sets in the spheres of computational geometry, convex analysis, discrete geometry, probability theory, game theory, etc.
• Topology: It pertains to the properties of a geometric object that demand continuous mapping. It has various applications in proximal continuity, proximity spaces, separation axioms, and uniform spaces.

#### Angles in Geometry

There are four types of angles in geometry:

• Acute angle – An acute angle is an angle that falls between 0 and 90 degrees.
• Obtuse angle – An obtuse angle is more than 90 degrees but less than 180 degrees.
• Right angle – An angle of 90 degrees is known as a right angle.
• Straight angle – A straight angle is 180 degrees, determined by a straight line.

A quadrilateral refers to a four-sided 2D figure, the sum of whose internal angles is 360°. The name quadrilateral is derived from two Latin words, ‘quadri’ and ‘latus,’ meaning four and side, respectively. It becomes pivotal to distinguish the properties of quadrilaterals to establish their differences from polygons. It can also be used in the construction of quadrilaterals. There are two basic properties of quadrilaterals:

• A quadrilateral always has four sides.
• The sum of all four internal angles of a quadrilateral is always 360°.

There are five types of quadrilaterals:

• Parallelogram
• Rectangle
• Square
• Rhombus
• Trapezium

#### Symmetry and Symmetrical Shapes

A shape is termed symmetrical when it is the same on both sides where lines can be drawn to show both sides are equal; whereas, a shape has symmetry when a mirror line can get drawn on it that reflects both sides are same or equal.

#### Conclusion

In a nutshell, geometry helps calculate the area, perimeter, volume, and various measures using the length, breadth, and height of different geometrical figures. There are a plethora of ways used in geometry in solving numerous complex problems. Geometry is easy to learn, and with practice, one can easily excel.

#### FAQs

1. What are the basic elements of geometry?
There are three basic elements of geometry:

• Point
• Line
• Plane
2. What does geometry mean?
In layman language, geometry refers to the measurement of Earth. The word ‘Geometry’ has been derived from the two Greek words—‘geo’ meaning Earth and ‘metron’ meaning measurement. Anything that you see around has its shape, which is called geometry.
3. What are some applications of geometry?
Having practical knowledge of geometry can help in various ways. Some of the applications of geometry include:

• Measurement of a line and surface area of land.
• To measure the dimensions of the land.
4. Is geometry easier than algebra?
Geometry is easier to understand and comprehend as compared to algebra. When it comes to algebra, it is more related to the complex equation, and Geometry is focused on finding the length of shapes and the measure of angles. Geometry is easy to apprehend and fun to learn.

Geometry is a division of mathematics that analyses the sizes, shapes, positions, angles, and dimensions. To understand better, you can refer to the video library by MSVgo that offers a detailed explanation of each topic. To know more about related topics, download the MSVgo app from the iOS App Store, Google Play Store, or visit the website https://msvgo.com/. Happy Learning!

### 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
• 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
• 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
• 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 – 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
• 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
• 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

• 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