# Chapter 6 – The Triangle and its Properties

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

Introduction

A polygon with three sides is called a triangle (tri = three). It is a closed structure with three sides, three vertices, and three angles. The triangles and their properties help to distinguish them into different types. It includes the sum of interior angles, and angle sum property of a triangle. There are many types of triangles, however, two special triangles: equilateral and isosceles, show the properties mentioned above but vary in the sides.

#### Medians of a Triangle

Take a plain paper and cut a triangle out of it. Try to fold this triangle into two equal parts; you will see a line connecting the two vertices. This is called the median of a triangle. A median connects a vertex of a triangle to the midpoint of the opposite side. It helps to study the triangle and its properties.

#### Altitudes of a Triangle

Cut a triangle from a hardboard and place it on your table. The height of the triangle from its tip to the base is called the altitude of a triangle. Altitude is perpendicular to the base of the triangle. So, one endpoint of altitude is at the vertex of the triangle, and another on the opposite side.

#### Exterior Angle of a Triangle and its Property

Take a look at ΔABC (in the figure). The angle located on the outside of the triangle is called the exterior angle of a triangle. And the angles inside the triangle are called interior angles of the triangle. The exterior angle of a triangle is equal to the sum of its opposite interior angles. This is also called the exterior angle property of a triangle.

Source: Class 7 Maths NCERT

For example:

∠ACD = Exterior angle of a triangle

∠BAC and ∠ABC = Interior angles of the triangle

From the exterior angle property of a triangle, ∠ACD = ∠BAC + ∠ABC

#### Angle Sum Property of a Triangle

Suppose, we cut a triangle on paper and measure all the interior angles. We tear the triangle into three parts, each carrying one angle. If you rearrange the pieces and calculate the sum of the angles, what do you observe? Before and after tearing the triangle, the sum of all the interior angles is 180°.

According to the Angle Sum Property of a Triangle, the total measure of the three angles of a triangle is 180°.

#### Two Special Triangles: Equilateral and Isosceles

With the help of a scale, draw a triangle having all equal sides. Such a triangle will be termed an equilateral triangle, where each angle measures 60°.

Source: Class 7 Maths NCERT

Draw another triangle with two sides that are equal and the third side unequal. Such a triangle is called an isosceles triangle. In an isosceles triangle, base angles opposite to the equal sides are equal.

Source: Class 7 Maths NCERT

#### Sum of the Lengths of Two Sides of a Triangle

Draw a triangle randomly without an exact measurement of the sides. Now measure each side and find the sum of any two sides. What did you get? You will observe that the sum of the lengths of any two sides of a triangle is always greater than the length of the third side. Now, try to subtract the length of any two sides. You will observe that the difference between the lengths of any two sides is smaller than the length of the third side.

#### Right-angled Triangles and Pythagoras Property

Draw a triangle with one right angle, i.e., 90 degree. Such a triangle will be termed a right-angled triangle. In this diagram, the right angle is ∠ABC.

Source: Class 7 Maths NCERT

In a right-angled triangle, the side opposite to the right angle is called the hypotenuse (in the figure, AC), and the other two sides are called its legs (here, AB and AC). All the right-angled triangles show Pythagoras property. If the triangle isn’t the right angle, this property isn’t valid. Hence, you can check whether it is a right-angled triangle or not.

According to Pythagoras property:

The square on the hypotenuse = the sum of the squares on its legs

AC² = AB² + BC²

#### Conclusion

All the triangles (acute, obtuse, or right-angled, equilateral, isosceles, or scalene) are polygons with an altitude and median. The Triangle and its Properties are highly specific, including angle sum property and exterior angle property. The Pythagoras property is exclusive to right-angled triangles.

#### FAQs

1. What are a triangle and its properties?
A triangle is a polygon with three sides, three angles, and three vertices. The properties of triangles are:
a) The sum of all internal angles of a triangle is equal to 180 degree.
b) The exterior angle of the triangle is equal to the sum of its interior opposite angles.
2. What are the three properties of a triangle?
a) The sum of all internal angles of a triangle is equal to 180 degree, i.e., angle sum property.
b) The exterior angle of the triangle is equal to the sum of its interior opposite angles, i.e., exterior angle property.
c) The sum of the lengths of any two sides of a triangle is always greater than the third side’s length.
3. What is triangle in class 7?
A triangle is a simple closed curve made of three line segments.

4. What are the properties of right-angle triangles?
a) A right-angle triangle has one angle called a right angle, i.e., 90 degree.
b) The side opposite to the right angle is called the hypotenuse, which is the longest side.
c) The other two sides adjacent to the hypotenuse are called Base and Perpendicular.
d) The sum of the remaining two interior angles is equal to 90 degree.
5. What are the seven types of triangles?
Triangles can be classified based on sides and angles. The seven types of triangles are:

1. Equilateral
2. Acute-angled isosceles
3. Obtuse-angled isosceles
4. Right-angled isosceles
5. Acute-angled scalene
6. Obtuse-angled scalene
7. Right scalene triangle

For more information about the triangle and its properties, check out MSVgo, a video library with lectures and animated videos. It has been developed to help students embark on conceptual learning among students from grades 6-12 for the CBSE, ICSE, ISC, IGCSE, and IB curriculum.

### 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
Please switch to portrait mode
for the best experience.