CBSE Class 8 Maths Chapter 3: Understanding Quadrilaterals NCERT Solutions

Reviewed by · Updated on

NCERT Solutions PDF Class 8 PDF

CBSE Class 8 Mathematics Chapter 3, Understanding Quadrilaterals, introduces students to the fascinating world of four-sided figures. This chapter focuses on the essential properties of quadrilaterals and helps students develop a clear understanding of various geometric shapes. We begin by exploring different types of curves, distinguishing between simple curves and simple closed curves. Then, we move on to polygons, learning to differentiate between convex and concave polygons based on their characteristics. The NCERT Solutions offer a systematic, step-by-step guide to classifying figures according to these definitions. Mastering these foundational concepts is vital for building a robust understanding of geometry and will significantly enhance problem-solving abilities, preparing students effectively for examinations.

Home

Quick info

BoardCBSE
ClassClass 8
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 3: Understanding Quadrilaterals

Chapter summary

Chapter 3, Understanding Quadrilaterals, focuses on introducing students to basic geometric shapes. The NCERT Solutions cover the classification of figures into simple curves, simple closed curves, polygons, convex polygons, and concave polygons. Students will practice identifying these shapes based on their visual characteristics and definitions, which is essential for further study in geometry.

Learning outcomes

  • Understand the definitions of simple curves, simple closed curves, polygons, convex polygons, and concave polygons.
  • Classify given figures based on the properties of curves and polygons.
  • Identify polygons from a set of given figures.
  • Distinguish between convex and concave polygons.

Topics covered

Paper topics

  • Simple Curve
  • Simple Closed Curve
  • Polygon
  • Convex Polygon
  • Concave Polygon
  • Classification of Figures
  • Geometric Shapes
  • Quadrilaterals Introduction

Important topics

  • Polygon
  • Convex Polygon
  • Concave Polygon
  • Classification of Curves
  • Classification of Polygons

PDF preview

Read page by page below. PDF is streamed from the official NCERT website — no download button on this page.

Loading document …
Page of
Loading page …

Questions and Solutions

Question 1

Given here are some figures. Classify each of them on the basis of the following:
  1. Simple curve
  2. Simple closed curve
  3. Polygon
  4. Convex polygon
  5. Concave polygon
(Note: Please refer to your NCERT textbook for the figures corresponding to numbers 1 through 8.)
Solution:

Let's classify the given figures based on the provided categories:

  1. Simple curve: A simple curve is a curve that does not intersect itself. Figures that fit this description are:
    • Figure (1)
    • Figure (2)
    • Figure (5)
    • Figure (6)
    • Figure (7)
  2. Simple closed curve: A simple closed curve is a curve that does not intersect itself and has no endpoints. Figures that fit this description are:
    • Figure (1)
    • Figure (2)
    • Figure (5)
    • Figure (6)
    • Figure (7)
  3. Polygon: A polygon is a closed figure made up entirely of straight line segments. Figures that fit this description are:
    • Figure (2)
    • Figure (1)
    • Figure (4)
  4. Convex polygon: A convex polygon is a polygon where all interior angles are less than 180 degrees, and all diagonals lie completely inside the polygon. From the polygons identified, Figure (1) is a convex polygon.
    • Figure (1)
  5. Concave polygon: A concave polygon is a polygon where at least one interior angle is greater than 180 degrees (a reflex angle), and at least one diagonal lies outside the polygon. From the polygons identified, Figures (4) and (1) (if considered with a re-entrant angle) can be concave. However, based on typical representations, Figure (4) is clearly concave, and Figure (1) is convex. If Figure (1) in the source was intended to represent a concave shape, it would have an inward bend. Assuming standard representations:
    • Figure (4)
    (Note: The classification of Figure (1) as concave depends on its specific drawing, but it is typically shown as convex. Figure (4) clearly exhibits concavity.)

Common mistakes

  • Confusing simple curves with simple closed curves.
  • Incorrectly classifying figures as polygons when they are not closed or are made of curves.
  • Difficulty in differentiating between convex and concave polygons based on diagonal properties.

Revision tips

  • Review the definitions of each type of curve and polygon thoroughly.
  • Practice classifying the figures in Exercise 3.1 multiple times.
  • Draw your own examples of convex and concave polygons to solidify understanding.
  • Focus on the key characteristics that define each classification.

Practice MCQs

Q1. Which of the following is a simple curve?

Q2. A polygon is a simple closed curve made up of only:

Q3. Which figure represents a convex polygon?

Q4. A polygon that has at least one interior angle greater than 180 degrees is called a:

Q5. Figure (2) from the given options is classified as:

Frequently asked questions

What is the main focus of Chapter 3: Understanding Quadrilaterals for Class 8 Maths?

This chapter introduces students to the basic concepts of geometric shapes, focusing on classifying curves and polygons, including simple curves, simple closed curves, polygons, convex polygons, and concave polygons.

How do these NCERT Solutions help students understand quadrilaterals?

The solutions provide clear, step-by-step classifications of various figures based on their geometric properties, helping students grasp the definitions and apply them to identify different types of curves and polygons.

What is the difference between a convex and a concave polygon?

A convex polygon has all interior angles less than 180 degrees, and all its diagonals lie inside the polygon. A concave polygon has at least one interior angle greater than 180 degrees, and at least one diagonal lies outside the polygon.

Are the figures in the exercise provided with the solutions?

The solutions refer to figures mentioned in the NCERT textbook's Exercise 3.1. Students should refer to their textbook to see the figures being classified.

Why is it important to classify curves and polygons?

Classifying geometric shapes helps in understanding their properties and relationships, which is fundamental for studying more advanced geometry and problem-solving.

Important links

Content reviewed by the NCERT Help team. Editorial Team and update policy

NCERT Solutions PDF PDF on NCERT Help. URL unchanged for search indexing.