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. 

2.0CBSE 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. 

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. 

Solution: 

According to Figure

∠ HDA + ∠EAB + x + ∠GCD = 360°

50° + 115° + x + 90° = 360°

255° + x = 360°

x = 360° - 255°

$\mathrm{x}=105°.$

Kinds and Properties of Quadrilaterals 

Parallelogram 

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

$AB=CD\text{ and }AD=BC$

2. Opposite angles of the parallelogram are equal to each other. 
3. 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. 
4. 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. 

3. 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. 

3.0Solved 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. 

Solution: 

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

∠ABC = 70 

∠ADC + ∠BAD = 180

∠BAD = 180 - 70

∠BAD = 110. 

2. 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°

4.0Key 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.