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Chapter 14 – Symmetry

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

Introduction

You may have heard of the term symmetry several times. But do you know that it can be explained mathematically as well? No! It has nothing to do with the symbols of addition, subtraction, multiplication or division. Stand before a mirror. What do you see? Well, you will find an identical image of yourself reflected on the other sides. The two are proportionate, and that is symmetry. You may also try to draw an imaginary line through your body longitudinally. The two halves can be described as mirror images of each other that are totally similar in all aspects. It gives you a sense of uniformity too. Well, that is referred to as symmetrical objects.

Think about different shapes used in mathematics. When you see a shape being duplicated fully after it is moved or turned or flipped to the opposite side, it is a symmetrical representation. Take some time to draw a heart on paper. Now fold it lengthwise or cut it in half longitudinally only to find two halves of the same image on either side. Now that is symmetry! It is found in all uniform patterns present in nature. You can go ahead and create many symmetrical objects in your Arts & Crafts class too. A shape that cannot be divided into two identical halves is known to be asymmetrical.

You may want to draw a line right through the middle of a figure you have created to fold it into two exact halves. However, you cannot make use of a pencil and draw the line physically every time. Instead, you have to imagine the line to divide a particular shape symmetrically. This line that divides an object into two halves is known as a line of symmetry. While you can draw it vertically, you can also draw a horizontal or diagonal line to meet your objective. Remember that you are free to have multiple lines of symmetry for a single figure as well. Here are a few examples to help you understand the concept better:

    • 1 Line – You can divide a figure symmetrically around a single axis. Look at the word “ATOYOTA.” You can draw a line through ‘Y’ to obtain two identical halves.
    • 2 Lines – A figure can be made symmetrical by passing a couple of lines through it. You can do it using a vertical and a horizontal line passing through the letters H and X.
    • Infinite Lines– You may pass as many lines as you want through certain figures to get symmetrical parts. The most obvious example here is a circle. Since no specific lines are forming the figure, you can divide it into multiple symmetrical parts by passing infinite lines through it.

If you think about other geometrical figures apart from a circle, then you will find it interesting to note that the closed figures known as polygons can be divided symmetrically as well. Think of a triangle; it has three sides. You can divide an equilateral triangle into symmetrical halves with the help of a line. A square can be divided similarly by two diagonal lines. You are welcome to use multiple lines of symmetry to divide other polygons such as pentagon, hexagon, heptagon, octagon and so on.

You can get a symmetrical figure when you rotate a figure, move it to another position or flip it completely. Symmetry is of four different types described based on varied situations:

    • Translation– When an object slides about an axis, the movement is known as translation. The object moves down in the same orientation and remains the same in shape and size.
    • Rotational– When you turn an object around a point, it becomes identical to itself even in position. The rotational symmetry line is therefore, a point. The angle of rotational symmetry is quite small for a figure to coincide with itself. Almost all polygons can have rotational symmetry with other objects such as petals displaying properties of symmetry and rotational symmetry too.
    • Reflection– Reflexive symmetry is described as a situation where a half of the object reflects the other completely. It can also be described as a mirror image. The two longitudinal halves of a human body or a butterfly can serve as classic examples of reflection symmetry.
    • Glide- A combination of reflection and translation symmetry can be described as glide symmetry. It has commutative properties that reinforce the theory that even if the objects’ order is altered, the results remain the same. You will learn more of this in higher classes once you get introduced to calculus and theories of probability.

You will have much fun trying to identify symmetry in different shapes. Take a figure depicting half a fish horizontally, for instance. You can make use of reflexive symmetry to complete the figure by obtaining a full fish. Use rotational symmetry to draw a flower of uniform proportions. You also have to remember that not all figures happen to be symmetrical. You will come across a scalene triangle in geometry and other irregular objects in nature that do not conform to the theory of symmetry.

The idea of symmetry may be pretty obvious, but you need to examine the world around you to understand the implications and mathematical reasoning behind it. You will find it easier to organize things once you master the concept and realize how symmetry enables us to create a harmonious effect.

  1. What are the 4 types of symmetry?
    The four types of symmetry are Translation, Rotational, Reflexive and Glide.
  2. What is symmetric in math?
    A figure, shape or object that can be divided into identical parts is known as a symmetric in mathematics.
  3. What is symmetry and its types?
    A shape that becomes exactly like the first one after it is moved, flipped or rotated is known as symmetry. It can be defined to be a mirror image of the original shape. Symmetry can be divided into 4 distinct types, namely translation, rotational, reflexive and glide.
  4. What is symmetry pattern?
    A pattern that produces uniformity and regularity with the shapes having different orientations is known to be a symmetrical pattern.
  5. Why is symmetry important in math?
    Learning symmetry in math helps students understand uniformity in nature and the abstract concepts of advanced mathematics later on in life. Connecting mathematics to other branches of study becomes simpler for the students too.

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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
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  • 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
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  • Equilibrium
  • Ethers and Carbonyl compounds
  • Haloalkanes and Haloarenes
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  • Ideal solutions
  • Introduction to Organic Chemistry
  • Ionic equilibria
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  • Matter Around Us
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  • Periodic Classification of Elements
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  • 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
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  • 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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