Grade 8
  1. Number Systems  1.1. Rational Numbers  1.2. Irrational Numbers  1.3. Real Numbers  1.4. Properties of Real Numbers  1.4.1. Commutative Property  1.4.2. Associative Property  1.4.3. Distributive Property  1.5. Representation on the Number Line  1.6. Operations on Real Numbers  1.6.1. Addition and Subtraction  1.6.2. Multiplication and Division  1.7. Rationalization  1.8. Exponents and Powers  1.9. Square Roots and Cube Roots
  2. Algebra  2.1. Algebraic Expressions  2.2. Identities and Simplification  2.2.1. Multiplying Binomials  2.2.2. Using Algebraic Identities  2.3. Factorization  2.3.1. Common Factors  2.3.2. Factorization by Grouping  2.3.3. Factorization of Trinomials  2.3.4. Special Products  2.4. Linear Equations in One Variable  2.4.1. Solving Linear Equations  2.4.2. Word Problems on Linear Equations
  3. Geometry  3.1. Understanding Quadrilaterals  3.1.1. Properties of Quadrilaterals  3.1.2. Types of Quadrilaterals  3.1.2.1. Parallelogram  3.1.2.2. Rectangle  3.1.2.3. Square  3.1.2.4. Rhombus  3.1.2.5. Trapezium  3.2. Constructions  3.2.1. Constructing Quadrilaterals  3.2.2. Constructing Bisectors  3.2.3. Constructing Angles  3.2.4. Constructing Triangles  3.3. Symmetry and Transformations  3.3.1. Reflection  3.3.2. Rotation  3.3.3. Translation  3.3.4. Symmetry in Patterns
  4. Mensuration  4.1. Area and Perimeter  4.1.1. Perimeter of Polygons  4.1.2. Area of Triangles  4.1.3. Area of Quadrilaterals  4.1.4. Area of Circles  4.2. Surface Area and Volume  4.2.1. Cubes  4.2.2. Cuboids  4.2.3. Cylinders  4.2.4. Cones  4.2.5. Spheres
  5. Data Handling  5.1. Organizing Data  5.2. Frequency Distribution Tables  5.3. Graphical Representation of Data  5.3.1. Bar Graphs  5.3.2. Histograms  5.3.3. Pie Charts  5.3.4. Line Graphs (added)  5.4. Probability  5.4.1. Introduction to Probability  5.4.2. Experimental Probability
  6. Coordinate Geometry  6.1. Cartesian Plane  6.2. Plotting Points  6.3. Coordinate System  6.4. Distance Between Points  6.5. Applications of Coordinate Geometry
  7. Introduction to Graphs  7.1. Linear Graphs  7.2. Applications of Graphs  7.3. Distance-Time Graphs  7.4. Speed-Time Graphs
  8. Comparing Quantities  8.1. Ratio and Proportion  8.2. Percentage  8.2.1. Increase and Decrease Percent  8.2.2. Discount in Percentage  8.2.3. Profit and Loss in Percentage  8.2.4. Simple Interest  8.2.5. Compound Interest
  9. Exponents and Powers  9.1. Laws of Exponents  9.2. Negative Exponents  9.3. Standard Form  9.4. Applications of Exponents
  10. Introduction to Squares and Square Roots  10.1. Properties of Square Numbers  10.2. Finding Square Roots  10.2.1. Prime Factorization Method  10.2.2. Division Method  10.3. Estimating Square Roots
  11. Introduction to Cubes and Cube Roots  11.1. Properties of Cube Numbers  11.2. Finding Cube Roots  11.2.1. Prime Factorization Method in Finding Cube Roots

Grade 8 → Geometry → Constructions ↓


Constructing Quadrilaterals


In geometry, a quadrilateral is a polygon with four sides and four vertices. Quadrilaterals can take many forms, such as squares, rectangles, trapezoids, and parallelograms. In Class 8 Maths, drawing quadrilaterals is an essential skill. The aim of this lesson is to guide you in drawing different types of quadrilaterals using basic tools like ruler and compass.

Basic properties of quadrilaterals

Before we move on to the construction, it is important to understand the basic properties of a quadrilateral. Here are the essential properties:

  • A quadrilateral has four sides.
  • The sum of the interior angles of a quadrilateral is always 360 degrees.
  • They have two diagonals.

Tools for construction

To draw a quadrilateral you will need some basic tools commonly used in geometry:

  • Ruler: For measuring and drawing straight lines.
  • Compass: For drawing arcs and circles.
  • Protractor: For measuring angles.
  • Pencil: For marking and drawing lines.

Let's start by constructing some common types of quadrilaterals.

Building a square

A square is a type of quadrilateral with four equal sides and four right angles. Follow these steps to draw a square:

  1. Draw a line segment AB of length 5 cm using a ruler.
  2. Set the width of the compass to 5 cm and draw an arc above the line AB, with the compass point A in it.
  3. With the same compass width, draw a second arc placing the compass at point B which will intersect the first arc at C.
  4. Draw a line segment AC and BC.
  5. Use the compass again to find point D by intersecting the arcs from A and C.
  6. Draw lines AD and CD.

The figure constructed is a square ABCD.

Constructing a rectangle

A rectangle is a quadrilateral with equal opposite sides and four right angles. Here's how you can draw a rectangle:

  1. Draw a line segment AB of length 6 cm.
  2. At point A, construct an angle of 90 degrees using a protractor and mark point C at a distance of 4 cm from A.
  3. At point B, again construct an angle of 90 degree using protractor and mark point D at a distance of 4 cm from B.
  4. Draw line segments CD and AD to complete the rectangle ABCD.

Construction of parallelogram

A parallelogram is a quadrilateral in which the opposite sides are parallel and equal in length. Here is how to construct it:

  1. Draw a line segment AB of length 6 cm.
  2. Choose a point D such that AD = 4 cm and draw an angle of your choice.
  3. Draw a line segment AD.
  4. Using a compass, draw an arc from B with a radius equal to AD.
  5. From D draw another arc of radius equal to AB which will intersect the previous arc at C.
  6. Connect point C to B and D.

Construction of trapezium

A trapezoid is a quadrilateral with at least one pair of parallel sides. Below is a guide to drawing a trapezoid:

  1. Draw a parallel line segment AB and place it at 5 cm.
  2. At each end point (A and B), use a compass to draw an arc above the line.
  3. Intersect these arcs at points C and D to complete the trapezoid.
  4. Draw the end sides CD and DA to complete the trapezium ABCD.

Understanding diagonals in a quadrilateral

Diagonals are important elements of a quadrilateral. A diagonal is a line segment joining two non-adjacent vertices. For squares and rectangles, the diagonals are equal in length. In a parallelogram, the diagonals bisect each other. In a trapezoid, there is no specific diagonal property, but they play an important role in the internal structure of the trapezoid. Understanding these properties helps in constructing and solving quadrilateral problems.

Angles in a quadrilateral

The sum of the interior angles of any quadrilateral is 360 degrees. If three angles are known, you can calculate the missing angle. Here is a simple formula:

angle_d = 360° - (angle_a + angle_b + angle_c)

Consider a quadrilateral ABCD whose angles are A, B, C, D. If you know three of these angles, you can find the fourth angle using this formula.

Construction of special quadrilaterals

In addition to the basic shapes, some quadrilaterals have special properties such as rhombuses and kites. Here is a guide to drawing them:

Construction of rhombus

A rhombus, like a square, has four sides equal, but not necessarily right angles. Draw it like this:

  1. Draw a line segment AB equal to the length of the desired side of the rhombus.
  2. Using a compass, draw arcs of equal length from both A and B.
  3. Intersect these at C and D.
  4. Draw lines AC, BC, AD, and BD.

Making a kite

In a kite, two pairs of adjacent sides are equal. Here is how to make a kite:

  1. Draw a diagonal AC of 7 cm.
  2. Draw two arcs of length 5 cm and 3 cm from A and C respectively. Intersect them at B.
  3. From A and C draw another set of arcs of length 3 cm and 5 cm respectively, and intersect at D.
  4. Draw lines AB, BC, CD and DA.

Conclusion

Drawing quadrilaterals is an important skill in geometry that allows you to explore various properties and relationships within shapes. Using simple tools like a ruler, compass, and protractor, you can draw a variety of quadrilaterals, from simple rectangles and squares to more complex rhombuses and kites. Understanding the basic properties of these shapes, such as congruence of sides, parallelism, and sum of angles, is essential to effectively draw and understand these geometric shapes.


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Constructing Quadrilaterals

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