CBSE Class 8 Maths Chapter 3: Understanding Quadrilaterals NCERT Solutions

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NCERT Solutions PDF Class 8 PDF

CBSE Class 8 Mathematics Chapter 3, "Understanding Quadrilaterals," introduces students to the fascinating world of geometric shapes. This chapter focuses on the basic properties and different types of quadrilaterals and other polygons. You'll learn to differentiate between simple curves, simple closed curves, and polygons. The solutions explore the distinctions between convex and concave polygons, providing clear definitions and examples. Understanding these classifications is key to identifying shapes based on their sides, vertices, and diagonals. This chapter builds a solid foundation in geometry, helping you to visualize and understand the characteristics of various figures, which is essential for tackling more complex geometric problems and succeeding in your exams.

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Quick info

BoardCBSE
ClassClass 8
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 3

Chapter summary

NCERT Solutions for Class 8 Maths Chapter 3, "Understanding Quadrilaterals," focuses on introducing students to the basic types of curves and polygons. It covers the classification of figures into simple curves, simple closed curves, polygons, convex polygons, and concave polygons. The solutions guide students through identifying these properties in various given figures, ensuring a clear understanding of geometric terminology and classification criteria.

Learning outcomes

  • Understand the definitions of simple curves, simple closed curves, and polygons.
  • Identify and classify polygons as convex or concave.
  • Apply classification criteria to given geometric figures.
  • Differentiate between various types of quadrilaterals and their properties.

Topics covered

Paper topics

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

Important topics

  • Understanding Polygons
  • Convex vs. Concave Polygons
  • Classifying Geometric Figures
  • Properties of Simple Curves

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Questions and Solutions

Question 1

Given here are some figures:

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Classify each of these figures on the basis of the following criteria:

  1. Simple curve
  2. Simple closed curve
  3. Polygon
  4. Convex polygon
  5. Concave polygon
Solution:

Let's classify each figure based on the given criteria:

  1. Simple curve: A curve is called simple if it does not intersect itself. Figures that are simple curves are: 1, 2, 5, 6, 7, 8.
  2. Simple closed curve: A simple curve that is closed is called a simple closed curve. Figures that are simple closed curves are: 1, 2, 5, 6, 7, 8.
  3. Polygon: A polygon is a simple closed curve made up of only line segments. Figures that are polygons are: 1, 2, 4.
  4. Convex polygon: A convex polygon is a polygon where all interior angles are less than 180 degrees, and all diagonals lie inside the polygon. Figure 1 is a convex polygon.
  5. Concave polygon: A concave polygon is a polygon where at least one interior angle is greater than 180 degrees, and at least one diagonal lies outside the polygon. Figures 4 and 1 (as it can be interpreted with an inward dent) are concave polygons. Note: Figure 1 is typically considered convex, but if interpreted with an inward vertex, it could be concave. Figure 4 is clearly concave.

Common mistakes

  • Confusing simple curves with simple closed curves.
  • Incorrectly classifying polygons as convex or concave.
  • Misidentifying figures that do not meet the criteria for a polygon.

Revision tips

  • Review the definitions of each type of curve and polygon thoroughly.
  • Practice classifying the figures provided in the exercise multiple times.
  • Draw your own examples of convex and concave polygons to solidify understanding.
  • Focus on the key distinguishing features for each classification.

Practice MCQs

Q1. Which of the following figures is a simple curve?

Q2. A polygon that is also a simple closed curve is:

Q3. Which figure represents a convex polygon?

Q4. Figure 4 is classified as a:

Q5. Which of the following is NOT a polygon?

Frequently asked questions

What is the main focus of CBSE Class 8 Maths Chapter 3?

Chapter 3, 'Understanding Quadrilaterals,' focuses on introducing students to the basic definitions and classifications of curves and polygons, including simple curves, simple closed curves, convex polygons, and concave polygons.

How do these NCERT Solutions help students?

These solutions provide clear, step-by-step explanations for classifying various geometric figures according to the definitions in the chapter, helping students grasp the concepts and solve related problems accurately.

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 all polygons simple closed curves?

Yes, by definition, a polygon is a type of simple closed curve made up entirely of straight line segments.

Can a simple curve be a polygon?

No, a simple curve can be made of line segments or curves. A polygon specifically must be a closed figure made up only of straight line segments that do not intersect except at the vertices.

Important links

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