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Chapter 6 – Triangles

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

Introduction

You might have come across an enclosed shape with three pointed tips; it is known as a triangle. A triangle is a polygon shape with three vertices and three edges. Being an enclosed shape with three sides, a triangle also has three angles whose sum is always 180 degrees. Triangle is one of the basic shapes in geometry. There are two ways to categorize triangles: the length of their sides or by their angle. Classifying triangles based on length are derived: isosceles triangle, equilateral triangle, and scalene triangle.

On the other hand, the three sorts of triangles derived based on their angles are acute angle triangle, right-angle triangle, and obtuse angle triangle. The perimeter for all sorts of triangles is the sum of all three sides of the same. For more information on a triangle, check video lectures on MSVgo. There, you can also learn ways to solve mathematical questions related to triangles.

A scalene triangle is the type of triangle whose all three sides tend to have different lengths and different angles. Some of the right-angled triangles are scalene if the other two angles and sides are not congruent. Due to this reason, no line of the scalene triangle is in symmetry. Additionally, the angle opposite the longest side is generally the largest angle, while the small side’s angle is the smallest. Lack of symmetry is the key feature of this sort of triangle. The formula for calculating a scalene triangle area is half times the product of its height and base length. For more information on this sort of triangle, go through the resource library on MSVgo.

The triangle with two equal sides and two equal angles is known as an isosceles triangle. The name ‘isosceles’ is derived from two Greek words: Iso, meaning same, and Skelos means legs. In an isosceles triangle, there are two same base angles with one other angle. The area of an isosceles triangle is calculated with the formula (b/4) * √(4a2 – b2), and its altitude is calculated with the formula (b/2a) * √(4a2 – b2). Key examples of isosceles triangles seen in the modern world are the faces of bipyramids and most of the Catalan solids. Since ancient times, the isosceles triangle was used in architecture and design to structure the pediments and gables of the constructed buildings. For more information on this sort of triangle, go through the resource library on MSVgo.

The equilateral triangle’s basic nature is that it has three equal sides and three congruent angles of F degrees. If a perpendicular is drawn from its vertex, the opposite sides are bisected into equal halves. The ortho-center and centroid of the equilateral triangle are always at the same point. The area of an equilateral triangle is derived with formula √3a2/4, where a is the side. Additionally, the median, angle bisector, and altitude of the sides of the equilateral triangle are always the same. For more information on this sort of triangle, go through the resource library on MSVgo.

A triangle whose all three angles are less than 90 degrees is known as an acute angle triangle. The formula for calculating an acute angle triangle area is half the product of base and height, while its perimeter is the addition of the length of all three sides. Equilateral triangles are always acute angle triangles as all its angles are 60 degrees. Additionally, if a line is drawn from the acute angle triangle base to the opposite vertex, it is always perpendicular to the base. For more information on this sort of triangle, go through the resource library on MSVgo.

The right-angle triangle is the triangle whose one angle is 90 degrees. This sort of triangle is the most used shape in mathematics due to its implications in Pythagoras theorem and trigonometry. Concerning the Pythagoras theorem, the right angle triangle depicts that hypotenuse is always the root of the sum of the squares of the base side and perpendicular side. On the other hand, the right-angle triangle is used in trigonometry as it always reflects the presence of three angles in the first quadrant due to the 90 degrees angle; thus, the values of sine, cos, and tan are derived easily using it. The first quadrant also reflects positive values, and the only sin, cos, and tan are positive in the first quadrant, while they change the value in the other three quadrants. Right angle triangle can be scalene or isosceles but never equilateral triangle as one of its angles is 90 degrees. For more information on this sort of triangle, go through the resource library on MSVgo.

An obtuse angle triangle is a triangle with one obtuse angle and two acute angles. There can be only one obtuse in a triangle because the sum of all the angles for a triangle is 180, and as per the definition of the obtuse angle, it is higher than 90 degrees. Thus, having two angles greater than 90 degrees will take the sum of the three angles to more than 180 degrees. For more information on this sort of triangle, go through the resource library on MSVgo.

Overall, the triangle is an enclosed geometrical shape with three sides, three angles, and three vertices. There are key basic types of triangles: the scalene triangle, isosceles triangle, and the equilateral triangle. There are three other sorts of triangles: acute angle triangle, right-angle triangle, and obtuse angle triangle.

What are the six types of triangles?

The six types of triangles are scalene triangle, isosceles triangle, equilateral triangle, acute angle, triangle, right-angle triangle, and obtuse angle triangle.

What are the three main types of triangles?

The three main types of triangles are scalene triangle, isosceles triangle, and equilateral triangle.

What are the five properties of a triangle?

The five properties of a triangle are:

  • It has three sides
  • It has three vertices
  • It has three angles
  • The sum of the internal angles of a triangle is always 180°.
  • The area of a triangle equals half the product of its height and base

What are congruent triangles in geometry?

If two angles and the included side of one triangle are similar to the corresponding constraints of another triangle, then both the triangles are said to be congruent.

For more fun and interactive lessons on Triangles, visit the MSVgo application.

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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