# Chapter 4 – Geometry

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

Introduction

Have you ever wondered why the things we see around us are shaped in a way they are? Geometry is a branch of mathematics concerned with the forms, angles, measurements, and proportions of a wide range of objects seen in daily life. There are two-dimensional and three-dimensional forms of Euclidean geometry.

Two forms, such as triangles, squares, rectangles, and circles, are referred to as flat shapes in plane geometry. Solids are 3D forms such as a square, cuboid, cone, and others in solid geometry. Points, lines, and planes are the fundamental elements of geometry. Geometry’s many forms of shapes assist us in comprehending the basic geometrical ideas we see in daily life. We can measure the area, circumference, and volume of shapes using geometric principles.

#### Types of Angles

Angles are classified into five categories depending on their direction. These five kinds of angles are the most popular in geometry:

1. Acute Angles: An acute angle is one that sits between 0 and 90 °, or in other terms, one that is less than 90 °.
2. Obtuse Angles: The inverse of an acute angle is an obtuse angle. An obtuse angle is one that is greater than 90 ° but less than 180 °, or in other terms, one that is greater than 90 ° but less than 180 °.
3. Right Angles: A 90-degree angle is often a right angle.
4. Straight Angles: As examined, a straight angle is 180 °.
5. Reflex Angles: A reflex angle is any angle that is > than 180 ° but < than 360 ° (which is the same as 0 °).

The following are examples of quadrilaterals:

• Convex: A quadrilateral’s diagonals are both entirely embedded inside a figure.
• Concave: A quadrilateral that has at least one diagonal that is partially or completely outside of the figure.

#### Measure of Line Segment

A line segment is bounded by two distinct points on a line in geometry. A line segment is a section of a line that links two lines. A line has no endpoints and may stretch in all directions indefinitely, while a line section has two fixed or definite endpoints.

A line segment may be measured by different methods which are:

• Method of observation
• Method using trace paper
• Method using ruler and divider

#### Measure of Angles

An angle is formed by two rays of the same endpoint. The vertex is the place where the two converge. The angle is a component of a hypothetical circle. There are four different kinds of angles. Knowing the discrepancy will help you approximate the angle measurement.

• Acute Angle
• Straight Angle
• Right Angle
• Obtuse Angle

A protractor is a perfect tool for measuring angles. Begin by aligning one ray with the protractor’s 0-degree axis. Then, align the vertex with the protractor’s midpoint. To find the angle’s measurement to the nearest degree, follow the second light.

#### Construction of Circle

A circle is a two-dimensional figure which is closed and all its points in the plane are at equal distances from a single point known as the “centre.” The line of reflection symmetry is formed for any line that moves around the circle. For any angle, it often has symmetry (rotational) around the middle.

#### What is the best way to draw a circle?

• Place a single point on an empty sheet of paper, somewhere in the centre of the sheet, and mark it as point A.
• Choose a random distance for the radius, such as 5 cm.
• Hold the reference zero mark on point A and mark 5 cm away from point A in both directions with a ruler.
• Mark as many points as you like away from point A, but they must all be within 5 cm of point O.
• If you choose enough points, you’ll find that the form begins to imitate a circle.

#### Symmetry Constructions

In geometry, students think about various geometrical forms, how they are constructed, and how to calculate them. Shapes may have a line of symmetry, regardless of whether they are geometrical or non-geometrical.

#### What is a Symmetry Line?

The hypothetical line that divides a figure into two parts that are mirror reflections of each other is called the line of symmetry. That is, they are precisely splitting the image into two equal bits. Those two sections are the same size and shape as another component.

#### Conclusion

In conclusion, geometry is angles, measurements, and proportions of a wide range of objects. There are five kinds of angles which are Acute Angles, Obtuse Angles, Right Angles, Straight Angles and Reflex Angles. A line segment is measured by method of observation, method using trace paper, method using ruler and divider.

#### FAQs

1. What are some of the fundamentals of geometry?
Three fundamental geometrical principles underpin all other geometrical concepts. The point, line, and plane are the three fundamentals.
2. Who was the first to invent geometry?
Euclid was a brilliant mathematician who was named the “Father of Geometry” by many.
3. What is the concept of geometry?
Geometry is a field of mathematics that explores how objects are measured in terms of their proportions, forms, angles, and dimensions. 2D forms are simple shapes such as squares, rings, and triangles that are part of flat geometry.
4. What role does geometry play in nature?Geometry helps us in deciding what materials to use, what design to make and also plays a vital role in the construction process itself.
5. What is the most powerful shape?
The triangle is a geometrical shape. The triangle is the most powerful formation, it is able to maintain its shape and provide a solid foundation.

### 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