Download Symmetrical Designs – NCERT Class 5 Maths Chapter 10 PDF from the new NCERT Class 5 Maths book Maths Mela (2026-27). Read the chapter online or download the free PDF. A line of symmetry is a folding line. Draw a line on a picture and fold the paper along it. If the two halves sit exactly on top of each other, that line is a line of symmetry. A shape that has at least one such line is said to have reflection…
Symmetrical Designs PDF – Chapter 10 of Maths Mela
Read the chapter online or download the PDF.
| Chapter | Download | |
|---|---|---|
| Chapter 10 PDF | Symmetrical Designs | View PDF |
| Full book | NCERT Class 5 Maths – Maths Mela | View Book |
Read Online
What Is in Symmetrical Designs? (Class 5 Maths Chapter 10)
- A line of symmetry is a folding line. Draw a line on a picture and fold the paper along it. If the two halves sit exactly on top of each other, that line is a line of symmetry. A shape that has at least one such line is said to have reflection symmetry — one half is the mirror image of the other half.
- That is why half a letter is enough. The letter A has one line of symmetry, standing straight up. So fold a paper once, draw only the left half of A along the fold, cut, and open. The fold makes the other half for you. This is the trick Prem and Manu use.
- Two lines mean a quarter is enough. The letter H has two lines of symmetry — one standing up (vertical) and one lying flat (horizontal). Fold the paper twice, draw only one-fourth of H along the folds, cut, and open. You get the whole H.
- Some shapes look the same when you turn them. Hold a shape at its centre and turn it. If it looks exactly the same before you have finished a full turn, it has rotational symmetry. A firki (paper windmill) has 4 blades. Turn it a quarter turn and it looks the same again. So a firki looks the same at 1/4, 1/2, 3/4 and full turn — 4 times in one full turn.
- A quarter turn, a half turn, a three-quarter turn. One full turn takes the shape all the way round and back. Half of that is a 1/2 turn (the shape ends upside down). One-fourth of a full turn is a 1/4 turn (a quarter of the way round). Every shape looks the same after a full turn, so a full turn does not count as symmetry by itself.
- The two symmetries are different, and a shape may have one, both or none. The letter N looks the same after a 1/2 turn but has no folding line — rotational only. The letter V has a folding line but never looks the same until a full turn — reflection only. The letters H, X and O have both. The letter K has a folding line only.
- Digits have symmetry too. In the book the digit 1 is printed as a plain straight bar. So 1, 0 and 8 look the same in a mirror and after a 1/2 turn. The digit 3 has a flat (horizontal) folding line. Numbers made from these digits behave the same way: 11 and 1001 look the same in a mirror and also after a half turn.
- You can build symmetry. Take a design that is not symmetrical and add shapes until each side matches the other. For a 1/2-turn design, every piece needs a partner directly opposite it. For a 1/4-turn design, all four arms must be exactly alike.
Quick revision – Symmetrical Designs
| Word | What it means | Where it appears | Example |
|---|---|---|---|
| Symmetry | When a shape looks the same after folding it or after turning it | Chapter title, page 136 | A butterfly’s two wings match |
| Line of symmetry | The folding line — fold along it and the two halves sit exactly on each other | Alphabet Cutout, page 136 | The line straight down the middle of A |
| Reflection symmetry | The shape has at least one line of symmetry; one half is the mirror of the other | Page 136 | V, T, E, K, X, O |
| Vertical line of symmetry | A line of symmetry that stands straight up | Page 136 | A, T, V, X, O |
| Horizontal line of symmetry | A line of symmetry that lies flat, across the shape | Page 136 | E, K, X, O |
| Rotational symmetry | The shape looks the same after a part-turn, before a full turn is over | Page 138 | H looks the same after a 1/2 turn |
| Full turn | Turning a shape all the way round, back to where it started | Pages 137–138 | The firki after a full turn |
| 1/2 turn | Half of a full turn — the shape ends upside down | Page 138 | N looks the same after a 1/2 turn |
| 1/4 turn | One-fourth of a full turn — a quarter of the way round | Page 137 | The firki looks the same after a 1/4 turn |
| Firki | A paper windmill made from a square sheet, cut and folded | Let Us Make a Windmill Firki, page 137 | It looks the same 4 times in a full turn |
| Centre | The fixed point you turn the shape about — marked with a red dot in the book | Page 138 | The middle of the letter X |
| Block printing | A craft of Rajasthan: a carved wooden block is dipped in colour and stamped on cloth | Let Us Explore, page 140 | One leaf block stamped 4 times |
| Design | A picture or pattern you make from shapes | Making Designs, page 139 | Squares and triangles put together |
Old NCERT vs New – Class 5 Maths
This chapter is from Maths Mela, the new NCERT Class 5 Maths book (NCF-SE 2023, used from 2025-26). It replaced the old book “Math-Magic”, so chapter numbers and names differ from older PDFs.
Solutions and All Chapters
Answers to the exercises and the full chapter list of Maths Mela:
Symmetrical Designs – Overview
| Class | Class 5 |
| Subject | Maths |
| Book | Maths Mela – new NCERT book |
| Chapter | 10 of 15 – Symmetrical Designs |
| Book pages | 136 – 141 |
| Edition | NCERT Reprint 2026-27 |
| Session | 2026-27 |
| Free – read online or download |
Class 5 Maths Chapter 10 – FAQs
Where can I download Symmetrical Designs Class 5 PDF?
From the download table on this page – the chapter PDF is free, and the full book is linked too.
What is Class 5 Maths Chapter 10 about?
A line of symmetry is a folding line. Draw a line on a picture and fold the paper along it. If the two halves sit exactly on top of each other, that line is a line of symmetry. A shape that has at least one such line is said to have reflection symmetry — one half is the mirror image of the other half.
Is Symmetrical Designs from the new NCERT Class 5 Maths book?
Yes. It is chapter 10 of maths mela, the new NCERT Class 5 Maths book for 2026-27.
Is this the latest NCERT edition for 2026-27?
Yes – the PDF is NCERT’s latest edition for the 2026-27 session.
Where are the NCERT Solutions for Class 5 Maths Chapter 10?
Open the NCERT Solutions link above for answers to the exercise questions.