# Chapter 10 – Practical Geometry

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

Introduction

Practical geometry is a part of geometry that deals with the study of shapes, size, dimensions, and positions of different objects. Geometry helps us to draw and define different figures and shapes.

When you want to draw a line segment, you take the help of a scale to measure the line and draw a straight line. When you want to draw a circle, you use a compass or a round object to outline it. These tools are geometrical tools that help us draw different shapes, figures, and objects. Practical geometry has both 2D and 3D objects and shapes.

#### Construction of a Line Parallel to a Given Line Through a Point Not on the Line

Steps:

1. Draw a line P and mark a point A outside of the line.
2. Take any other point, say Q, and join the lines PQ.
3. Now take B as a centre and take a radius of 4 cm.
4. Cut an arc on line P at C and AB.
5. Mark the intersection point as D on AB.
6. With A as a centre now and the same radius as before, cut an arc EF to cut AB at G.
7. Measure the arc length CD by placing a pointed tip of the compass at C and pencil tip opening at D.
8. With this opening, keep G as a centre and draw an arc to cut arc EF at H.
9. Join AH to draw a line Q.

∠ABC and ∠BAH are alternate interior angles. Therefore, P || Q.

#### Construction of a Triangle

Triangles can be constructed and classified based on two major concepts:

1. Sides:
Equilateral triangle: All three sides are equal.
Isosceles triangle: Two sides are equal.
Scalene triangle: All three sides are equal.
2. Angles:
Acute triangle: All angles measure less than 90 degree.
Obtuse triangle: One angle is greater than 90 degree.
cRight triangle: One angle is equal to 90 degree.

#### Constructing a Triangle When the Lengths of its Three Sides are Known (SSS Criterion)

Construct a triangle DEF, given that DE = 7.6 cm, EF = 4.5 cm, and DF = 8.6 cm.

Steps:

1. Draw a line segment EF of length 4.5 cm.
2. Draw an arc of a radius 7.6 cm with E.
3. Draw an arc of radius 8.6 cm with F.
4. Mark the intersection of both the arcs with point D.
5. Join the line segment DE and DF.
6. You will get a triangle DEF.

#### Constructing a Triangle When the Lengths of Two Sides and the Measure of the Angle Between Them are Known (SAS Criterion)

Construct ΔLMN with LM = 6.4 cm, LM = 5.5 cm, and ∠M = 45 degree.

Steps:

1. Draw a line segment LM of length 6.4 cm.
2. At point M, draw a line segment MX with an angle of 45 degree with LM.
3. Take point M as the centre, measure an arc of 5.5 cm.
4. Draw an arc of 5.5 cm that cuts MX at point Y.
5. Join MN.

#### Constructing a Triangle When the Measures of Two of its Angles and the Length of the Side Inclined Between Them is Given (ASA Criterion)

Construct ΔPQR with ∠P = 40o, ∠Q = 100 degree, and XY = 7.2 cm.

Steps:

1. Draw a line segment PQ of length 7.2 cm.
2. At point P, draw a ray named PA marking an angle of 40 degree with PQ.
3. At point Q, draw an angle of 100 degree with PQ.
4. Draw the line segment QR.
5. Extend the ray PA to intersect QR at point B.
6. The point at which both the lines PA and QR intersect is point B.
7. ΔABC is now complete.

#### Constructing a Right-Angled Triangle When the Length of One Leg and its Hypotenuse are Given (RHS Criterion)

Construct ΔABC, with ∠B = 90 degree, BC = 6 cm, and AC = 10 cm.

Steps:

1. Draw a line segment BC of length 6 cm.
2. At point B, draw BX ⊥ BC, which is perpendicular to each other.
3. To cut BX at point A with C as the centre, draw an arc of radius 10 cm.
4. Join AC.
5. ΔABC is complete.

#### FAQs

1. What is practical geometry?
Practical geometry is a part of geometry that deals with the study of shapes, size, dimensions, and positions of different objects.
2. What is geometry in simple words?
Geometry is the branch of mathematics related to the study of sizes, shapes, and distances of different figures and objects. Shapes of 2D and 3D are also studied in geometry.
3. What is the use of geometry?
Geometry is used in mapping, architecture, interior design, medical operations, and surgeries, etc.
4. What are the three types of geometry?
The three types of geometry are Euclidean, Spherical, and Hyperbolic.
5. How do you do practical geometry?
Practical geometry is practised by constructing different shapes, figures, and measurements.

Here we learned what practical geometry in class 7 is. We explored the construction of triangles, the perpendicular bisector of a triangle, and the construction of similar triangles.  To clarify more of your doubts about the construction of triangles class 7, download MSVgo. It is a video library that explains concepts with examples, explanatory visualisations, and animations in a fun manner.

### High School Physics

• Alternating Current
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• Dual nature of Radiation and Matter
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• Electricity
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### High School Chemistry

• Acids, Bases and Salts
• Alcohols, Phenols and Ethers
• Aldehydes, Ketones and Carboxylic Acids
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### High School Biology

• Absorption and Movement of Water in Plants
• Anatomy of Flowering Plants
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• Breathing and Exchange of Gases
• Cell – Unit of Life
• Cell Cycle and Cell Division
• Cell Division and Structure of Chromosomes
• Cell Reproduction
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• 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
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• Improvement In Food Resources
• Integumentary System- Skin
• Kingdom Fungi
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• 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