NCERT Solutions for Class 5th Maths Chapter 10 Symmetrical Designs
Updated on 2026-09-19
About this chapter
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. So
- Prem and Manu cut letters for Lali's birthday wall
- Paper cutouts of the pictures printed on the border
- Lali's firki, and what happens when you turn it
- 2 3 4 5 6 7 8 9 0, and the numbers 11 and 1001
- The blue design of triangles and circles
- Making designs from squares and equilateral triangles
- Four blue squares with a triangle on each side
- Matching the wooden blocks of Rajasthan to their prints
- Design A (the leaf cross) and design B (the four hearts)
- Symmetrical patterns with vegetable blocks
Quick revision
| 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 |
Exercises
- Prem and Manu cut letters for Lali's birthday wall — Alphabet Cutout Page 136
- Paper cutouts of the pictures printed on the border — Let Us Do Page 136
- Lali's firki, and what happens when you turn it — Let Us Make a Windmill Firki Page 137
- The table of letters H, I, X and Y at 1/4, 1/2, 3/4 and full turn — Turning the Letters Page 138
- 2 3 4 5 6 7 8 9 0, and the numbers 11 and 1001 — Let Us Do — Find symmetry in the digits Page 1381
- The blue design of triangles and circles — Making Designs Page 139
- The green-and-pink square, and colouring a square for a 1/4 turn — Let Us Think Page 139
- Making designs from squares and equilateral triangles — Let Us Do Page 139
- Four blue squares with a triangle on each side — Symmetry in a Shape Page 140
- Matching the wooden blocks of Rajasthan to their prints — Let Us Explore — Block Printing Page 140
- Design A (the leaf cross) and design B (the four hearts) — The Print Made by One Block Page 141
- Tick the shapes with reflection symmetry, star the ones with rotational symmetry — Let Us Do — Shapes on the border Page 141
- Symmetrical patterns with vegetable blocks — Project Work Page 141