Posted by RBSE Solutions for Class 6 Maths Chapter 13: Symmetry introduces students to the concept of symmetry, a fundamental aspect of geometry. This chapter covers types of symmetry, including line symmetry and rotational symmetry, and helps students understand how symmetrical shapes can be identified and drawn. The solutions provided help students visualize and solve symmetry-based questions with ease.
Key Concepts Covered in Chapter 13: Symmetry
- Introduction to Symmetry
- Types of Symmetry: Line and Rotational
- Identifying Symmetrical Figures
- Drawing Lines of Symmetry
- Real-Life Examples of Symmetry
Learning about symmetry helps students understand the balance and aesthetics in both natural and human-made structures.
Detailed RBSE Class 6 Solutions for Chapter 13: Symmetry
Below are detailed, question-wise solutions for Chapter 13, designed to provide step-by-step explanations. These solutions make symmetry concepts easy to understand, building a strong foundation in geometric properties.
NCERT Solutions for Class 6 Chapter 13: Symmetry Exercise 13.1
Table of Contents
1. List any four symmetrical objects from your home or school.
Solutions:
Four symmetrical objects are the blackboard, the tabletop, a pair of scissors and the computer disc.
2. For the given figure, which one is the mirror line, l1 or l2?
Solutions:
l2 is the mirror line of the figure. When the given figure is folded along the line l2, the left part exactly covers the right part and vice versa
3. Identify the shapes given below. Check whether they are symmetric or not. Draw the line of symmetry as well.
Solutions:
(a) Yes. It is symmetric
(b) Yes. It is symmetric
(c) No, it is not symmetric
(d) Yes. It is symmetric
(e) Yes. It is symmetric
(f) Yes. It is symmetric
The following figures given below show the lines of symmetry
4. Copy the following on a squared paper. A square paper is what you would have used in your arithmetic notebook in earlier classes. Then complete them such that the dotted line is the line of symmetry.
Solutions:
Making the dotted line a line of symmetry, the given figure may be drawn as follows
(a)
(b)
(c)
(d)
(e)
(f)
5. In the figure, l is the line of symmetry. Complete the diagram to make it symmetric.
Solutions:
The below figure is the complete diagram to make it symmetric
6. In the figure, l is the line of symmetry. Draw the image of the triangle and complete the diagram so that it becomes symmetric.
Solutions:
The required triangle may be drawn as follows to make it symmetric:
NCERT Solutions for Class 6 Maths Chapter 13 Symmetry Exercise 13.2
1. Find the number of lines of symmetry for each of the following shapes:
Solutions:
(a) For the given figure there are 4 lines of symmetry.
(b) For the given figure there are 4 lines of symmetry.
(c) For the given figure there are 4 lines of symmetry.
(d) For the given figure there is only 1 line of symmetry.
(e) For the given figure there are 6 lines of symmetry.
(f) For the given figure there are 6 lines of symmetry.
(g) For the given figure there is no line of symmetry.
(h) For the given figure there is no line of symmetry.
(i) For the given figure there are 3 lines of symmetry.
Now we may observe the lines of symmetry in the above figures as follows
2. Copy the triangle in each of the following figures on squared paper. In each case, draw the line(s) of symmetry, if any and identify the type of triangle. (Some of you may like to trace the figures and try paper-folding first!)
Solutions:
(a) The given triangle is an isosceles triangle. Here it will be only 1 line of symmetry.
(b) The given triangle is an isosceles triangle. Here it will be only 1 line of symmetry.
(c) The given triangle is a right angled triangle. Here it will be only 1 line of symmetry.
(d) The given triangle is a scalene triangle. Here it will be no line of symmetry.
3. Complete the following table.
Solutions:
The given table is completed as follows:
In case of circles we find infinite lines. Here some lines of symmetry are drawn. Similarly, we can draw more symmetric lines for the circle.
4. Can you draw a triangle which has
(a) exactly one line of symmetry?
(b) exactly two lines of symmetry?
(c) exactly three lines of symmetry?
(d) no lines of symmetry?
Sketch a rough figure in each case.
Solutions:
(a) Yes, we can draw an isosceles triangle which has only 1 line of symmetry.
(b) No, we cannot draw a triangle which has 2 lines of symmetry.
(c) Yes, we can draw an equilateral triangle which has 3 lines of symmetry.
(d) Yes, we can draw a scalene triangle which has no line of symmetry.
5. On a squared paper, sketch the following:
(a) A triangle with a horizontal line of symmetry but no vertical line of symmetry.
(b) A quadrilateral with both horizontal and vertical lines of symmetry.
(c) A quadrilateral with a horizontal line of symmetry but no vertical line of symmetry.
(d) A hexagon with exactly two lines of symmetry.
(e) A hexagon with six lines of symmetry.
Solutions:
(a) A triangle with a horizontal line of symmetry but no vertical line of symmetry can be drawn as follows
(b) A quadrilateral with both horizontal and vertical lines of symmetry can be drawn as follows
(c) A quadrilateral with a horizontal line of symmetry but no vertical line of symmetry can be sketched as follows
(d) A hexagon with exactly two lines of symmetry may be drawn as follows
(e) A hexagon with 6 lines of symmetry may be drawn as follows
6. Trace each figure and draw the lines of symmetry, if any:
Solutions:
(a) The given figure is an isosceles triangle. Hence, there will be 1 line of symmetry.
(b) The given figure has two lines of symmetry.
(c) The given figure has 4 lines of symmetry.
(d) The given figure is an octagonal which has 2 lines of symmetry.
(e) The given figure has only 1 line of symmetry.
(f) The given figure has 4 lines of symmetry.
7. Consider the letters of English alphabets, A to Z. List among them the letters which have
(a) vertical lines of symmetry (like A)
(b) horizontal lines of symmetry (like B)
(c) no lines of symmetry (like Q)
Solutions:
(a) Vertical lines of symmetry are A, H, I, M, O, T, U, V, W, X, Y.
(b) Horizontal lines of symmetry are B, C, D, E, H, I, K, O, X.
(c) No lines of symmetry are F, G, J, L, N, P, Q, R, S, Z.
8. Given here are figures of a few folded sheets and designs drawn about the fold. In each case, draw a rough diagram of the complete figure that would be seen when the design is cut off.
Solutions:
We may draw a diagram of complete figure as follows
NCERT Solutions for Class 6 Maths Chapter 13: Symmetry Exercise 13.3
1. Find the number of lines of symmetry in each of the following shapes. How will you check your answers?
Solutions:
(a) For the given figure, there are 4 lines of symmetry.
(b) For the given figure, there is only 1 line of symmetry.
(c) For the given figure, there are 2 lines of symmetry.
(d) For the given figure, there are 2 lines of symmetry.
(e) For the given figure, there is only 1 line of symmetry.
(f) For the given figure, there are 2 lines of symmetry.
2. Copy the following drawing on squared paper. Complete each one of them such that the resulting figure has two dotted lines as two lines of symmetry.
How did you go about completing the picture?
Solutions:
We can complete these figures by drawing similar parts as shown in these figures. First, about the vertical line of symmetry and then about the horizontal line of symmetry, or first about the horizontal line of symmetry and then about the vertical line of symmetry.
The completed figures are as follows:
3. In each figure alongside, a letter of the alphabet is shown along with a vertical line. Take the mirror image of the letter in the given line. Find which letters look the same after reflection (i.e., which letters look the same in the image) and which do not. Can you guess why?
Try for O, E, M, N, P, H, L, T, S, V and X.
Solutions:
The mirror images of these figures are as follows:
The letters having vertical lines of symmetry will have the same mirror images. The letters are O, M, H, T, V, and X, and thus, these letters will look the same.
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- RBSE Solutions for Class 6 Maths Chapter 13: Symmetry | Updated for 2024-25
- RBSE Solutions for Class 6 Maths Chapter 14: Practical Geometry | Updated for 2024-25
Benefits of RBSE Class 6 Chapter 13 Solutions
- Improved Visualization Skills: Students can better understand and recognize symmetry in different shapes.
- Enhanced Learning: Clear explanations make it easier to grasp abstract concepts of symmetry.
- Practical Application: Learning symmetry has real-life applications in art, design, and architecture.
FAQs on RBSE Solutions for Class 6 Maths Chapter 13: Symmetry
Q1: What is symmetry in mathematics?
A1: Symmetry in mathematics refers to a balanced and proportional arrangement of parts on opposite sides of a dividing line or around a central point.
Q2: What is line symmetry?
A2: Line symmetry, also known as reflectional symmetry, occurs when a shape can be divided by a line into two identical parts that are mirror images of each other.
Q3: What is rotational symmetry?
A3: Rotational symmetry is when a figure can be rotated (less than a full circle) about a central point and still look the same as it did before the rotation.
Q4: How does learning symmetry benefit students?
A4: Learning about symmetry improves spatial awareness, which is beneficial in art, design, engineering, and understanding the geometry of objects in the real world.
Q5: Where can I find detailed RBSE solutions for Class 6 Chapter 13?
A5: You can access comprehensive, step-by-step solutions on rbsesolution.in, where each question is explained for easy understanding.
Conclusion
The RBSE Solutions for Class 6 Maths Chapter 13: Symmetry provides students with a fundamental understanding of symmetry, which is a vital concept in geometry. Through these solutions, students can easily identify symmetrical shapes, draw lines of symmetry, and appreciate the role of symmetry in the natural and built environments. Practicing these solutions will enhance students’ spatial reasoning and prepare them for future geometry concepts.