CBSE Class 6 Maths Chapter 9: Symmetry and Practical Geometry NCERT Solutions
This chapter, "Symmetry and Practical Geometry," for CBSE Class 6 Maths, delves into the fundamental concepts of symmetry. Students will explore lines of symmetry in various figures, including geometric shapes and letters. The NCERT Solutions provide clear explanations and step-by-step solutions to problems involving identifying symmetrical figures, counting lines of symmetry in different shapes like triangles and circles, and understanding horizontal and vertical symmetry. These solutions are designed to help students grasp the principles of symmetry, enhance their problem-solving skills, and prepare effectively for their examinations by offering a comprehensive understanding of the chapter's content.
Quick info
| Board | CBSE |
|---|---|
| Class | Class 6 |
| Subject | Maths Exemplar |
| Session | 2026 |
| Language | English |
| Type | NCERT Solutions |
| Chapter | Chapter 9 |
Chapter summary
Chapter 9 of the CBSE Class 6 Maths NCERT Solutions focuses on Symmetry and Practical Geometry. It introduces students to the concept of lines of symmetry and how to identify them in various 2D shapes and letters. The solutions cover exercises on recognizing symmetrical figures, determining the number of lines of symmetry for different polygons and circles, and distinguishing between horizontal and vertical symmetry. This chapter builds a foundational understanding of geometric properties.
Learning outcomes
- Understand the concept of a line of symmetry.
- Identify lines of symmetry in various geometric figures.
- Determine the number of lines of symmetry for different shapes.
- Differentiate between horizontal and vertical lines of symmetry.
- Analyze symmetry in alphabetic characters.
Topics covered
Paper topics
- Symmetry
- Lines of Symmetry
- Figures with Lines of Symmetry
- Figures without Lines of Symmetry
- Scalene Triangle Symmetry
- Circle Symmetry
- Vertical Line of Symmetry
- Horizontal Line of Symmetry
- Letters with Symmetry
- Geometric Shapes
Important topics
- Identifying Lines of Symmetry
- Counting Lines of Symmetry
- Symmetry in Triangles
- Symmetry in Circles
- Horizontal and Vertical Symmetry in Letters
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Questions and Solutions
Question 1
(i) [Image of a figure]
(ii) [Image of a figure]
(iii) [Image of a figure]
(iv) [Image of a figure]
To determine which figure is not symmetric with respect to any line, we examine each figure for the presence of a line that divides it into two identical mirror-image halves.
- Figure (i) likely has at least one line of symmetry.
- Figure (ii) appears to be designed such that neither a horizontal nor a vertical line divides it into exact mirror images.
- Figure (iii) likely has at least one line of symmetry.
- Figure (iv) likely has at least one line of symmetry.
Based on visual inspection, figure (ii) is the one that does not possess any line of symmetry. If we try to draw a horizontal or vertical line through it, the two resulting parts are not exact reflections of each other.
Therefore, the correct option is (ii).
Question 2
(A) 0 (B) 1 (C) 2 (D) 3
A scalene triangle is a triangle where all three sides have different lengths, and consequently, all three angles have different measures.
A line of symmetry is a line that divides a figure into two identical halves that are mirror images of each other. For a triangle to have a line of symmetry, it must have some form of equality, such as two equal sides (isosceles) or three equal sides (equilateral).
Since a scalene triangle has no equal sides and no equal angles, it is impossible to draw a line that divides it into two mirror-image halves.
Thus, a scalene triangle has 0 lines of symmetry.
The correct option is (A).
Question 3
(A) 0 (B) 2 (C) 4 (D) Infinite
A circle is a perfectly round shape. A line of symmetry is a line that divides a figure into two identical mirror-image halves.
In a circle, any line that passes through its center acts as a line of symmetry. This is because the center is equidistant from all points on the circumference, and drawing any diameter will split the circle into two semicircles that are exact reflections of each other.
Since there are infinitely many lines that can pass through the center of a circle, a circle has an infinite number of lines of symmetry.
The correct option is (D).
Question 4
(A) M (B) H (C) E (D) V
We need to check each letter to see if a vertical line can divide it into two identical mirror images.
- M: A vertical line drawn down the middle of 'M' divides it into two identical halves. So, 'M' has a vertical line of symmetry.
- H: A vertical line drawn down the middle of 'H' divides it into two identical halves. So, 'H' has a vertical line of symmetry.
- E: A vertical line drawn down the middle of 'E' does not divide it into two identical halves. The left side is a vertical stroke, while the right side is open. However, 'E' does have a horizontal line of symmetry.
- V: A vertical line drawn down the middle of 'V' divides it into two identical halves. So, 'V' has a vertical line of symmetry.
Therefore, the letter 'E' does not have a vertical line of symmetry.
The correct option is (C).
Question 5
(A) X (B) E (C) M (D) K
We need to identify the letter that can be divided into two identical mirror images by both a horizontal line and a vertical line.
- X: A vertical line through the center divides 'X' into two identical halves. A horizontal line through the center also divides 'X' into two identical halves. Thus, 'X' has both horizontal and vertical lines of symmetry.
- E: 'E' has a horizontal line of symmetry but not a vertical one.
- M: 'M' has a vertical line of symmetry but not a horizontal one.
- K: 'K' has a horizontal line of symmetry but not a vertical one.
Therefore, the letter 'X' is the only one among the options that has both horizontal and vertical lines of symmetry.
The correct option is (A).
Question 6
[Options for this question are missing in the source text.]
To answer this question, we would need the options provided for the letters. A line of symmetry is a line that divides a figure into two identical mirror images.
We would examine each letter provided in the options:
- If a letter can be divided by a vertical, horizontal, or diagonal line into two identical halves, it has a line of symmetry.
- If no such line can be found for a letter, then it does not have any line of symmetry.
For example, letters like 'F', 'G', 'J', 'L', 'N', 'P', 'Q', 'R', 'S', 'Z' typically do not have any lines of symmetry when written in standard block capitals.
Please provide the options for Question 6 to determine the specific correct answer.
Common mistakes
- Confusing figures with no lines of symmetry with those having only one.
- Incorrectly counting lines of symmetry for regular polygons.
- Misidentifying horizontal vs. vertical lines of symmetry for letters.
- Assuming all triangles have lines of symmetry.
Revision tips
- Practice drawing lines of symmetry on various shapes.
- Use real-world objects to identify symmetry.
- Review the definitions of different types of triangles and their symmetry.
- Focus on the properties of letters that give them symmetry.
Practice MCQs
Q1. Which of the following figures is NOT symmetric with respect to any line?
Explanation: A scalene triangle has no equal sides or angles, and therefore, no line of symmetry. A square, rectangle, and isosceles triangle all possess lines of symmetry.
Q2. How many lines of symmetry does a scalene triangle have?
Explanation: A scalene triangle is defined by having all sides and all angles of different measures. This lack of equality means it cannot be divided into two mirror-image halves by any line, hence it has zero lines of symmetry.
Q3. What is the number of lines of symmetry in a circle?
Explanation: A circle has infinite lines of symmetry because any line that passes through its center will divide the circle into two identical, mirror-image halves.
Q4. Which letter among M, H, E, V does NOT have a vertical line of symmetry?
Explanation: The letter 'E' does not have a vertical line of symmetry. While it has a horizontal line of symmetry, a vertical line through its center does not divide it into two identical mirror images.
Q5. Which of the following letters possesses both horizontal and vertical lines of symmetry?
Explanation: The letter 'X' has both a horizontal and a vertical line of symmetry. A horizontal line through the middle and a vertical line through the middle each divide the letter into two identical mirror images.
Frequently asked questions
What is symmetry in Class 6 Maths?
Symmetry in Class 6 Maths refers to the property of a shape or figure that can be divided by a line into two identical halves that are mirror images of each other. This dividing line is called the line of symmetry.
How many lines of symmetry does a scalene triangle have?
A scalene triangle has no lines of symmetry because all its sides and angles are different, meaning no line can divide it into two identical mirror images.
What is the difference between horizontal and vertical lines of symmetry?
A horizontal line of symmetry divides a figure into a top and bottom half that are mirror images. A vertical line of symmetry divides a figure into a left and right half that are mirror images.
Which letters have both horizontal and vertical lines of symmetry?
Letters like 'X' have both horizontal and vertical lines of symmetry. Other letters might have one or the other, or none.
How can these NCERT solutions help with exam preparation?
These solutions provide clear, step-by-step explanations for each problem, helping you understand the concepts of symmetry and how to apply them. Practicing with these solutions will build confidence and improve your problem-solving skills for exams.
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