CBSE Class 6 Mathematics Chapter 13: Symmetry NCERT Solutions

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NCERT Solutions PDF Class 6 PDF

This chapter on Symmetry for Class 6 Mathematics, aligned with CBSE NCERT guidelines, introduces students to the fundamental concept of symmetry. The solutions cover identifying symmetrical objects, understanding the mirror line, and drawing lines of symmetry for various shapes. Students will learn to distinguish between symmetrical and asymmetrical figures and practice drawing lines of symmetry for given shapes. These solutions provide clear, step-by-step explanations to help students grasp the principles of symmetry, making it an excellent resource for exam preparation and reinforcing classroom learning.

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Quick info

BoardCBSE
ClassClass 6
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 13

Chapter summary

Chapter 13, Symmetry, for Class 6 Mathematics NCERT Solutions focuses on introducing the concept of symmetry and lines of symmetry. The exercises involve identifying symmetrical objects from daily life, determining the mirror line for given figures, and identifying whether various shapes are symmetric or not. Students are guided to draw the line(s) of symmetry for symmetrical shapes. This chapter builds foundational geometric understanding.

Learning outcomes

  • Understand the concept of symmetry in objects.
  • Identify symmetrical objects from the surroundings.
  • Distinguish between symmetrical and asymmetrical figures.
  • Identify the mirror line in a given figure.
  • Draw the line of symmetry for various simple shapes.

Topics covered

Paper topics

  • Symmetry
  • Mirror Line
  • Line of Symmetry
  • Symmetrical Objects
  • Identifying Symmetry
  • Drawing Lines of Symmetry
  • Geometric Shapes
  • Reflection

Important topics

  • Concept of Symmetry
  • Identifying Line of Symmetry
  • Symmetry in Geometric Shapes
  • Symmetry in Real-Life Objects

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Questions and Solutions

Question 1

List any four symmetrical objects that you can find in your home or school.
Solution: Symmetry is a property where an object looks the same even after a transformation like reflection or rotation. Many everyday objects exhibit symmetry. Here are four examples of symmetrical objects commonly found at home or school:
  1. A notebook (when closed, the line down the middle is a line of symmetry).
  2. A blackboard (it has a line of symmetry down the middle).
  3. A glass tumbler (many tumblers have a circular base and straight sides, showing rotational symmetry and often a vertical line of symmetry).
  4. An inkpot (often cylindrical or cubical, possessing symmetry).
These objects are symmetrical because they can be divided into two identical halves by a line or have a balanced appearance around a central point.

Question 2

For the given figure, determine which line, <math>l_1</math> or <math>l_2</math>, represents the mirror line.

Figure showing two lines l1 and l2 intersecting a shape.

<math>l_2</math>

Solution: The mirror line, also known as the line of symmetry, is a line that divides a figure into two identical halves that are mirror images of each other. In the given figure, line <math>l_2</math> acts as the mirror line because if you were to place a mirror along <math>l_2</math>, the reflection of one side would perfectly match the other side. Line <math>l_1</math> does not divide the figure into two identical halves. Therefore, <math>l_2</math> is the mirror line.

Question 3

Identify the shapes given below. For each shape, determine if it is symmetric or not. If it is symmetric, draw its line of symmetry.

(a)

(e) (f) (d)

Solution: Let's analyze each shape for symmetry:

  1. Shape (a): This shape is symmetric. The line of symmetry is a vertical line passing through the center, dividing the shape into two identical mirror-image halves.

    line of symmetry

  2. Shape (b): This shape is symmetric. The line of symmetry is a vertical line passing through the center, dividing the shape into two identical mirror-image halves.

    -line of symmetry

  3. Shape (c): This shape is not symmetric. There is no single straight line that can divide this shape into two identical mirror-image halves.

  4. Shape (d): This shape is symmetric. The line of symmetry is a vertical line passing through the center, dividing the shape into two identical mirror-image halves.

    -line of symmetry

  5. Shape (e): This shape is symmetric. It has a horizontal line of symmetry passing through its middle, dividing it into two identical halves.

    -line of symmetry

  6. Shape (f): This shape is symmetric. It has a vertical line of symmetry passing through its middle, dividing it into two identical halves.

    -line of symmetry

Common mistakes

  • Confusing the mirror line with other lines in a figure.
  • Incorrectly identifying shapes as symmetric when they are not.
  • Failing to draw all possible lines of symmetry for a shape.
  • Difficulty in visualizing the reflection across a line.

Revision tips

  • Practice identifying symmetry in everyday objects around you.
  • Use a mirror to check for symmetry in different shapes.
  • Carefully draw the lines of symmetry, ensuring they divide the shape into two identical halves.
  • Review the definitions of symmetry and mirror line before attempting problems.

Practice MCQs

Q1. Which of the following is an example of a symmetrical object from daily life?

Q2. In the context of symmetry, what does a mirror line represent?

Q3. Which of these shapes is NOT typically considered symmetric with a single vertical line of symmetry?

Q4. If a shape can be folded along a line so that the two halves match exactly, what is that line called?

Frequently asked questions

What is symmetry in Class 6 Maths?

Symmetry in Class 6 Mathematics refers to the property of an object or shape that looks exactly the same even after being reflected across a line or rotated by a certain angle. The line across which the reflection occurs is called the line of symmetry.

How can I identify the line of symmetry for a given shape?

To identify the line of symmetry, try to fold the shape. If you can fold it such that the two halves match perfectly, the fold line is the line of symmetry. For figures like circles, any diameter can be a line of symmetry.

Are all shapes symmetrical?

No, not all shapes are symmetrical. Some shapes have one or more lines of symmetry, while others have no lines of symmetry at all. For example, a square is symmetrical, but a random irregular shape might not be.

What are some examples of symmetrical objects from home or school?

Examples of symmetrical objects from home or school include a notebook (when closed), a blackboard, a glass tumbler, a window pane, and a clock face.

How do these NCERT Solutions help with exam revision?

These solutions provide clear, step-by-step explanations for each question in Chapter 13, helping students understand the concepts of symmetry and lines of symmetry. Practicing these solutions reinforces learning and builds confidence for exams.

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