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Chapter 4 – Practical Geometry

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

Introduction

You must have witnessed the real-life usage of geometrical figures while measuring the circumference, or area of a plot, the volume of a container, and so on. Practical geometry has significant usage in various recreational activities like sports, video games, and in the food design industry as well. It can be defined as the construction of various figures such as parallel lines, perpendicular lines, line segments, quadrilaterals, triangles, and others. Let us look into the various concepts of practical geometry.

Constructing a quadrilateral is possible when some of the parameters are provided. This includes:

A diagonal and 4 sides.

2 diagonals are provided with three sides.

2 adjacent sides provided with three angles.

3 sides are provided along with two included angles.

Any of the special properties of the quadrilateral is known.

All these points will become more clear in the step by step method of constructing it in the following example:

Case 1: 

4 sides and one diagonal is given.

Example:

Let ABCD be a quadrilateral with its sides AB= 4 cm, BC= 6 cm CD=5 cm and AD=5.5 cm and AC = 7 cm

First make a rough sketch of the figure with the length of the sides written, to be able to visualize it. The SSS construction condition can be used for drawing the triangle ABC. Locate the 4th point ‘D’ opposite to B with reference to AC which is 7 cm. Take A as the center and draw an arc of a 5.5 cm radius. The point D lies somewhere on this, which can be known by cutting another arc of 5 cm with ‘C’ as a center (as CD= 5 cm).

So ‘D’ will be the point of intersection of both the arcs. Now the quadrilateral ABCD can be completed.

Case 2: 

2 diagonals and 3 sides are provided.

Example:

Just like the previous case, we need to draw the triangle first with the provided parameters and then locate the 4th point.

Example:

The sides of a quadrilateral ABCD are BC= 4.5 cm, AD= 5.5 cm. and CV = 5cm. Its diagonals are AC= 5.5 cm and BD= 7 cm

So, first, we need to construct ACD using SSS theorem. As per the given data, B has to be at a distance of 4.5 cm from C and 7 cm from D. An arc has to be drawn from D with a 7 cm radius for locating point B’. Now, with a radius of 4.5 cm with C as the center, draw an arc.

The intersection of arcs drawn from point ‘A’ and ‘C’ is the point ‘B’, which completes our quadrilateral now.

Case 3:

Two adjacent sides and 3 angles of a quadrilateral are provided. 

Example:

In a quadrilateral ABCD where AB = 3.5 cm, BC = 6.5 cm,

∠A = 75°, ∠B = 105° and ∠C = 120°

Draw AB= 3.5 cm and  then the angle ∠B = 105°, BC= 6.5 cm.

Now draw ∠C = 120° and let us say this angle is ∠BCY = 120°.

Now draw ∠A = 75° and extend this line to meet the one emerging from ∠C,  and this intersection will be ‘D’

Case 4:

Given are the two sides with two included angles of a quadrilateral.

Example:

Let ABCD be a quadrilateral with sides AB = 4 cm, BC = 5 cm, CD = 6.5 cm and  angles ∠B = 105°, ∠C = 80°.

So we need to draw ∠B= 105°  at ‘B’ on the line AB= 4 cm. Let the line emerging from B after drawing the angle be ‘BX’.

Draw ∠C = 80° and extend the emerging line, let say CY on which ‘D’ will be located.

Mark 4 cm on ‘BX’ and name it as ‘BA’. Similarly mark ‘D’ on CY at 6.5 cm from ‘C’. Join A and D and the quadrilateral is complete.

Here are two special cases that you will learn in practical geometry class 8

i. Constructing a quadrilateral with just one measurement:

This is possible just in the case of a square which is a special quadrilateral with all equal sides and equal angles of 90 degrees each.

ii. Constructing a quadrilateral with just two measurements:

Rhombus falls in this special case. Its diagonals bisect each other at right angles. So it can be constructed by first drawing the diagonal, let’s say AC, finding its midpoint ‘o’, and then drawing a perpendicular at this point. Let ‘B’ and ‘D’ be the two points on the opposite sides of the diagonal AC such that OD and OB are of equal length, i.e 1/2 of BD.

By joining the points A, B, C, D we will get the required rhombus.

What is geometry in simple words?

Geometry can be defined as a branch in mathematics dealing with various sizes, shapes, dimensions, positions, and angles.  These can be two dimensional or three dimensional.

What are the 3 types of geometry?

There are 3 types of 2D geometry, namely, Euclidean, spherical, and hyperbolic.

How is geometry used in real life?

Geometry is used in real life in computer-aided designing for constructing blueprints, in manufacturing for designing the assembly systems, nanotechnology, creation of visual reality, video gaming programming, visual graphics, and computer graphics.

Why do we use geometry?

Geometry is used for deciding the materials that have to be used along with the perfect design. So it has a major role in the construction process. Similarly, it has important uses in the designing field also.*

How do you understand geometry? 

Geometry is an interesting topic in mathematics which can be understood by understanding the concepts so that you can solve different kinds of problems easily. A visual illustration with examples plays a major role in the process. You can get this from websites or apps like MSVGo that focuses on ensuring clarity of the students in core concepts.

What are 10 geometric concepts?

The 10 basic concepts of geometry are point, ray, line, line segment, plane, angles, parallel lines, intersecting lines, properties of angles in geometrical figures like sum of internal angles of triangle is 180 degrees and that of a quadrilateral is 360 degree.

Best source for learning practical geometry:

MSVGo is the best place for learning the concepts of practical geometry because it clearly explains them with different examples. The video library will help you to get better conceptual clarity through visual illustrations. Thus you won’t easily forget these during the exam and even afterwards.

This was a concise description of the concepts in practical geometry. For better understanding of the topic through visual illustrations you can refer to the MSVGo website or app that has a video library for explaining the concepts with visualisations and animations.

High School Physics

  • Alternating Current
  • Atoms
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High School Chemistry

  • Acids, Bases and Salts
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High School Biology

  • Absorption and Movement of Water in Plants
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High School Math

  • Algebra – Arithmatic Progressions
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  • Geometry – Quadrilaterals
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  • Trignometry – Height and Distance
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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
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  • Universe
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  • 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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