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CBSE Notes
Class 8
Maths
Chapter 3 Understanding Quadrilaterals

CBSE Notes For Class 8 Maths Chapter 3 Understanding Quadrilaterals

1.0Introduction to Quadrilaterals

A Quadrilateral is a four-sided polygon. In the word Quadrilateral, “Quad” means four while “lateral” means sides; combining them means the polygon with four sides. By knowing and understanding the key features of quadrilaterals, it will be easy to solve the geometric problems related to them. Here are some figures that are in the shape of quadrilaterals. 

Different Quadrilaterals

2.0Download CBSE Class 8 Maths Chapter 3 Understanding Quadrilaterals: Free PDF

Download the free PDF of CBSE Class 8 Maths Chapter 3 Understanding Quadrilaterals for easy and effective revision. This resource covers types of quadrilaterals, their properties, angles, and classifications as per the latest CBSE syllabus.

Class 8 Maths Chapter 3 Revision Notes:

3.0CBSE Class 8 Maths Chapter-3 Understanding Quadrilaterals - Revision Notes

Understanding the Basics 

Before starting to know about quadrilaterals, Let’s understand some basics of a polygon; there are types in maths and some of their properties: 

Line segments joining the sides and resulting in closed shapes are called polygons. There are two types: Regular polygons and irregular polygons. 

Regular Polygon

Irregular Polygon

A regular polygon has both equal sides and equal angles on all sides at the same time; for example, an equilateral triangle is a regular polygon. 

Irregular polygons either have all sides or an equal angle, but not both at the same time. An irregular polygon can also neither be of equal angles nor sides. 

Property:

The sum of all the exterior angles of a polygon is always equal to 360 degrees, no matter how many sides it has. 

Example: Find the value of x in the given figure. 

Problems on Quadrilaterals

Solution: 

According to Figure

∠ HDA + ∠EAB + x + ∠GCD = 360°

50° + 115° + x + 90° = 360°

255° + x = 360°

x = 360° - 255°

x=105°.

Kinds and Properties of Quadrilaterals 

Parallelogram 

  1. Opposite sides of a parallelogram are equal to each other.

AB=CD and AD=BC

  1. Opposite angles of the parallelogram are equal to each other. 
  2. Adjacent angles of two angles of the parallelogram are supplementary to each other, meaning the sum of 2 adjacent angles is equal to 180 degrees. 
  3. Diagonals of every parallelogram bisect each other, meaning they cut each other in equal lengths. 

Rhombus 

  1. All sides of the rhombus are equal and parallel to each other. 
  2. Diagonals bisect each other with the right angle.
  3. All the angles of the parallelogram are equal to each other. 
  4. All the rest of the properties of the rhombus resemble a parallelogram.

Rectangle 

  1. Opposite sides of the rectangle are equal & parallel to each other.
  2. Diagonals are equal to each other. 
  3. All the angles of the rectangle are equal to 90 degrees.
  4. The rest of the properties of the Rectangle resemble the Parallelogram.  

Square

  1. All the sides of a square are equal and parallel to each other. 
  2. Diagonals are equal and bisect each other at a right angle.
  3. All the angles of a square are equal to 90 degrees. 
  4. The rest of the properties of the square are equal to the parallelogram. 

Kite 

  1. The diagonals bisect each other at the right angle. 
  2. Two distinct sides of adjacent sides are equal in length. 

Kite

  1. One pair of opposite angles is equal to each other; that is, here,∠ ADC = ∠ ABC, but the other one is equal to each other, and the ∠ DAB is not equal to ∠DCA. 

4.0Solved Examples

Example 1: In the given figure, ABCD is a parallelogram. Given that the length of AD is 5 cm and AB is 4 cm. And ∠ADC is equal to 70 degrees. Find: 

  1. Angle ABC and BAD. 
  2. Length of side BC and DC. 

Sample question on parallelogram

Solution: 

  1. ∠ ADC = ∠ABC (Opposite angles of Parallelogram are equal)

∠ABC = 70 

∠ADC + ∠BAD = 180

∠BAD = 180 - 70

∠BAD = 110. 

  1. AD = BC 

     BC = 5 cm (Opposite sides of a parallelogram are equal)

    AB = CD 

     CD = 4 cm (Opposite sides of a parallelogram are equal)


Example 2: If AM and CN are perpendiculars on the diagonal BD of a parallelogram ABCD, Is ∆AMD ≅ ∆CNB?

Solution: In AMD and CNB

∠AMD = ∠CNB = 90

AD = BC (Opposite sides of a parallelogram) 

∠ADM = ∠CBN (Alternate interior angle) 

∆AMD ≅ ∆CNB (AAS)


Example 3: Find x in the following figure.

Solution: In the given figure ∠1 + 90° = 180° (linear pair) 

∠1 = 90° 

Now, the sum of exterior angles of a polygon is 360° therefore, 

x + 60° + 90° + 90° + 40° = 360° x + 280° = 360° 

x = 80°

5.0Key Features for CBSE Maths Notes Class 8 Chapter 3 

  • The notes are designed for quick reading and easy navigation to save time.
  • These notes provide a detailed & step-by-step guide to solving questions related to quadrilaterals. 
  • Illustrative diagrams help simplify and understand difficult concepts with ease. 
  • The content of the notes is frequently updated with respect to the latest CBSE curriculum.

Chapter-wise CBSE Notes for Class 8 Maths:

Class 8 Maths Chapter 1 - Rational Numbers Notes

Class 8 Maths Chapter 2 - Linear Equations In One Variable Notes

Class 8 Maths Chapter 3 - Understanding Quadrilaterals Notes

Class 8 Maths Chapter 4 - Data Handling Notes

Class 8 Maths Chapter 5 - Squares and Square Roots Notes

Class 8 Maths Chapter 6 - Cubes and Cube Roots Notes

Class 8 Maths Chapter 7 - Comparing Quantities Notes

Class 8 Maths Chapter 8 - Algebraic Expressions and Identities Notes

Class 8 Maths Chapter 9 - Mensuration Notes

Class 8 Maths Chapter 10 - Exponents and Powers Notes

Class 8 Maths Chapter 11 - Direct and Inverse Proportions Notes

Class 8 Maths Chapter 12 - Factorisation Notes

Class 8 Maths Chapter 13 - Introduction to Graphs Notes


Chapter-wise NCERT Solutions for Class 8 Maths All Chapters:-

Chapter 1: Rational Numbers

Chapter 2: Linear Equations in One Variable

Chapter 3: Understanding Quadrilaterals

Chapter 4: Data Handling

Chapter 5: Squares and Square Roots

Chapter 6: Cubes and Cube Roots

Chapter 7: Comparing Quantities

Chapter 8: Algebraic Expressions and Identities

Chapter 9: Mensuration

Chapter 10: Exponents and Powers

Chapter 11: Direct and Inverse Proportions

Chapter 12: Factorisation

Chapter 13: Introduction to Graphs

Frequently Asked Questions

A parallelogram has opposite sides, equal and parallel, but its angles do not have to be 90°. The diagonals bisect each other but are not equal. A rectangle is a parallelogram with an additional property: it contains four right angles; in other words, all of its angles are 90°. This means that the diagonals are the same length and bisect each other.

A kite, in maths, is a quadrilateral having two pairs of adjacent sides equal, while one diagonal bisects the other at right angles. A rhombus is a regular quadrilateral in which all the sides are equal; its diagonals bisect each other at right angles but need not be unequal.

All quadrilaterals have the same sum of interior angles that equals 360° regardless of the figure.

Yes, a rectangle whose all sides are equal is a square. Thus, all squares are rectangles, but vice versa is not always true, i.e., not all rectangles are squares.

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