# Chapter 4 – Geometry

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

Introduction

Geometry is the mathematics branch that deals with the forms, angles, measurements, and proportions of a number of ordinary objects we see. There are two-dimensional forms and three-dimensional forms in Euclidean geometry.

Two forms, such as triangles, squares, rectangles, rings, are often considered flat shapes in plane geometry. In solid geometry, solids are often referred to as 3d structures, such as a cube, cuboid, cone, etc. The simple geometry, explained in coordinate geometry, is based on points, lines, and planes.

The numerous kinds of shapes in geometry allow one to consider the shapes of daily life. We can measure the areas of parallelograms and triangles, their perimeter, and volume with the aid of geometric principles.

#### Geometry Branches

• Algebraic Geometry: is a geometry branch exploring multivariate polynomial zeros. This involves algebraic linear and polynomial equations that are used to solve the sets of zeros. This type of application consists of cryptography, string theory, etc.
• Discrete Geometry: The relative location of a simple geometric object, such as points, arcs, triangles, circles, etc., is concerned with it.
• Differential Geometry: using algebra and calculus methods for problem-solving. The different topics include general relativity in physics, etc.
• Euclidean Geometry: The analysis of plane and solid figures, including points, lines, planes, angles, congruence, resemblance, solid figures, focused on axioms and theorems. It has a wide variety of applications in computer science, problem-solving in modern mathematics, crystallography, etc. Also known as Euclid’s Geometry.
• Convex Geometry: includes Euclidean space convex forms using actual analysis techniques. It has an application in number theory for optimization and functional analysis.
• Topology: is concerned with the continuous mapping of space objects. Compactness, completeness, consistency, filters, function spaces, grills, clusters and bunches, hyperspace topologies, initial and final structures, metric spaces, nets, proximal continuity, proximity spaces, axioms of separation, and uniform spaces are considered in its implementation.

#### Geometry for Plane

Flat forms that can be drawn on a sheet of paper are dealt with by Plane Geometry. This involves two-dimension arcs, circles & triangles. Plane geometry is also known as the geometry of two dimensions. There are only two tests for all two-dimensional statistics, such as length and width. The width of the shapes does not interact with it. A cube, triangle, rectangle, circle, and so on are some examples of plane figures. Here, in plane geometry, some of the essential terminologies are clarified.

• Point: A point on a plane is a particular position or spot. Normally, a dot represents them. It is necessary to consider that a point is not an item, but a location. Also, note that there is no dimension to a point; it is ideally the only place.
• Line: The line is linear (no curves), has no thickness, and continues without ending in both directions (infinitely). It is necessary to remember that to form a line, it is the convergence of infinite points together. We have a horizontal line and vertical line in geometry, which respectively are x-axis and y-axis.

#### Polygons in Geometry

A plane figure that is connected to form a closed polygonal chain or circuit by a finite chain of straight line segments closing in a circle.

The term ‘poly’ extends to multiples. An n-gon is a polygon with n sides; a 3-gon polygon is, for instance, a triangle.

General Formula for Sum of a polygon’s interior angles

Sum of a polygon’s interior angles = (n-2) x 180

Polygon Types

The polygon types are:

• Triangles
• Quadrilaterals
• Pentagon
• Hexagon
• Heptagon
• Octagon
• Nonagon
• Decagon
 Polygon Type Definition and Property Triangles A 3-sided polygon that often adds up to  180 degrees to the number of internal angles. The area of a triangle can be found out using Heron’s Formula. Quadrilaterals A polygon of 4 sides with four corners and four vertices. 360 degrees sum of the number of internal angles Pentagon Having five straight sides and five angles, a plane figure Hexagon Having six straight sides and six angles, a plane figure Heptagon Having seven sides and seven angles, a plane figure Octagon Having eight straight sides and eight angles, a plane figure Nonagon Nine straight sides and nine angles for a plane figure. Decagon A figure of a plane of ten straight sides and ten angles.

#### Geometry Circle

A Circle is a closed, simple structure. Both points in a circle are the same consistent distance from a certain point called the center, i.e. the curve drawn out by a point that travels such that the distance from the center is fixed.

Congruence and Similarity

• Similarity: Whether they have the same outline or have an identical angle but do not have the same height, two figures are considered to be similar.
• Congruence: Since they have the same form and scale, two numbers are said to be congruent. They are therefore completely equivalent.

#### Conclusion

In this chapter, we learned about lines & angles, different shapes, and their geometry. We will apply this knowledge to solve questions based on surface areas & volumes and improvise our constructions of figures.

#### FAQs

1. What are the basics of geometry?

Three basic concepts depend on the fundamental geometrical concepts. The point, line, and plane are them. We can’t describe the terms specifically. But, it applies to the placemark and has a definite spot.

2. What are the 3 types of geometry?

There are 3 geometries in two dimensions: Euclidean, spherical, and hyperbolic. For 2-dimensional objects, these are the only geometries possible.

3. What are 10 geometric terms?

• Perpendicular Line Segments
• Right Angle
• Equilateral Triangle
• Scalene Triangle
• Vertex
• Right Triangle
• Pentagon
• Square
• Intersecting Line Segments
• Acute Angle

4. What are 10 geometric concepts?

The principles in geometry are points, lines, planes, angles, parallel lines, triangles, similarity, trigonometry, quadrilaterals, transformations, circles, and area.

5. How do we use geometry in real life?

In the real world, geometry uses include computer-aided design for building plans, assembly systems design in engineering, nanotechnology, computer graphics, visual graphs, programming for video games, and the development of virtual reality.

We understand that learning geometry can be tough. At MSVgo, we provide you with easy video lessons with real-life examples to understand it easily. Go ahead and try it out now! It’s entirely free to download on the Google Play Store as well as Apple iOS App Store.

### 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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