NCERT Solutions for Class 5 Mathematics Chapter 10 Symmetrical Designs

This worksheet provides NCERT Solutions for Class 5 Mathematics Chapter Symmetrical Designs. This chapter focuses on understanding symmetry through shapes, letters, numbers, and patterns. It helps students learn how figures look the same when folded or rotated. This worksheet includes complete and accurate NCERT Solutions that help students clearly understand key concepts like line symmetry and rotational symmetry in a simple and structured way.

Chapter summary: stories, poems & themes

This chapter is activity-based and focuses on visual and hands-on learning. Students explore symmetry using alphabet cutouts, shapes, numbers, and design-making activities. They learn through folding paper, rotating objects, and observing patterns. The main theme of the chapter is understanding how objects remain the same under reflection and rotation, making learning engaging and interactive.

What this NCERT chapter covers?

• Understanding line symmetry using horizontal and vertical lines  
• Learning rotational symmetry through turns like half and quarter turns  
• Identifying symmetry in alphabets and numbers  
• Creating symmetrical designs using shapes and patterns  
• Observing symmetry using folding and rotation activities  
• Developing visual and spatial understanding  

How to use these NCERT solutions?

Students should first try to solve each question on their own by observing the shapes and patterns carefully. After attempting, they can use these NCERT Solutions to check their answers and understand the correct approach. Parents and teachers can guide students by encouraging hands-on activities like folding paper and drawing symmetry lines. These solutions follow the NCERT structure and order, making them useful for revision and better concept clarity.

Student tips & learning tricks

• Always check symmetry by folding or imagining a fold line  
• For rotational symmetry, rotate the figure mentally and check if it matches  
• Pay attention to both horizontal and vertical symmetry lines  
• Practice drawing shapes carefully to improve accuracy  
• Common mistake: forgetting to check both reflection and rotation  

Why NCERT solutions are important?

NCERT Solutions help students build strong foundational concepts in mathematics. They provide step-by-step clarity aligned with CBSE standards. These solutions improve confidence, help in understanding concepts deeply, and prepare students for school assessments by following the exact NCERT pattern.

Complete answer key – NCERT solutions

Alphabet Cutout

1. Horizontal line of symmetry - E, X, O  
2. Vertical line of symmetry - T, V, O, X  
3. Both vertical and horizontal lines of symmetry - X, O  

Let Us Do

1. Explanation: Use folded paper to create symmetrical shapes like diya and boat. Draw half or a part along the fold, cut carefully, and open to see the full symmetrical design  
2. Answer: Yes, it looks the same at each turn. only the green dot changes its position.  

Rotational Symmetry (Letters Activity)

1. Yes, at 1/2 turn  
2. I, X not Y  

Let Us Make a Windmill Firki

1. X O  
2. E T  
3. X O  
4. E T VV  

Let Us Do

1. Horizontal line of symmetry 3  
2. Vertical line of symmetry 0, 1, 8  
3. Rotational symmetry: 1, 8, 0  

Examples

1. 3-digit: 101, 808  
2. Both rotational and reflection symmetries: 1, 8, 0  
3. Reflection symmetry: 0, 1, 3 (horizontally), 8  

Numbers

1. 2-digit: 11, 69 (rotational), 88  
2. 4-digit: 1001, 8008  

Explanation: Observe each digit carefully. Check by folding (reflection) or rotating (rotation) to see if it looks the same  

Making Designs

1. (a) No  
2. (b) Explanation: Add shapes so the design matches after half turn (180° rotation). Add a circle to the left of the figure  
3. (c) Explanation: Modify shapes so design matches after quarter turn (90° rotation). Add 2 more circles at top and bottom  
4. (d) Yes. Along the vertical and horizontal lines passing through the centre  

Explanation

1. Use square and triangle cutouts to form patterns. Arrange them so they look the same when folded or rotated. Draw symmetry lines where possible  
2. Draw lines along the horizontal and vertical axis centrally  
3. It has rotational symmetry at half of a turn  
4. Yes, it has reflection symmetry too  
5. Reflection symmetry: Yes  
6. Rotational symmetry: Yes  
7. Both: Yes  

Let Us Think

1. Yes  
2. No  
3. Diagram colored as shown. 4 times  
4. No reflective symmetry. Will have it only if adjacent triangles are of same color  

Let Us Explore

1. (i) – c  
2. (ii) – d  
3. (iii) – a  
4. (iv) – e (given)  
5. (v) – b  

Answer

1. 1/4 turn, Rotational and reflectional symmetry  

Let Us Do

1. Explanation: Create patterns using vegetable blocks. Repeat prints in order to form symmetrical designs. Observe whether designs match after rotation or reflection  

Project Work

1. student-generated activity  

Master symmetrical designs in Class 5 Mathematics with clear NCERT Solutions and build strong visual learning skills for better understanding and exam success.  
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