Class 5 Exam > Class 5 Notes > Mathematics (Maths Mela) Class 5 - New NCERT > Important Formulas: Symmetrical Designs
Important Formulas: Symmetrical Designs | Mathematics (Maths Mela) Class 5 - New NCERT PDF Download
1. Meaning of Symmetry
Symmetry means that when a shape is divided into two parts, both halves are identical (mirror images).
Symmetry creates balance, equality, and beauty in designs (e.g., butterfly wings, rangoli, flowers).
2. Reflection Symmetry
A shape has reflection symmetry if one half is the mirror image of the other half.
Line of Symmetry → The line dividing a figure into two equal mirror-image halves.
Types of Symmetry Lines:
Vertical – Line goes up and down.
Horizontal – Line goes left to right.
Multiple lines – Some shapes (e.g., square, circle) have more than one line of symmetry.
Examples with Alphabets:
Vertical symmetry: A, T, V, X, O
Horizontal symmetry: E, O, X
Both horizontal & vertical: X, O
3. Rotational Symmetry
A shape has rotational symmetry if it looks the same after turning around its centre (without a full 360° turn).
Order of Rotational Symmetry: The number of times a shape looks the same during one full 360° rotation.
Examples:
Square → order 4 (looks the same 4 times).
Rectangle → order 2.
Circle → infinite order.
Windmill firki → order 4.
4. Shapes with Both Reflection and Rotational Symmetry
Some shapes have both kinds of symmetry.
Example: Square
4 lines of reflection symmetry.
Rotational symmetry of order 4.
5. Symmetry in Digits & Numbers
Digits with reflection symmetry: 0, 1, 8
Digits with rotational symmetry: 0, 1, 8
Digits with both: 0, 1, 8
Examples of numbers with symmetry:
Reflection symmetry: 11, 181, 8008
Rotational symmetry: 69, 818, 609
Both symmetries: 11, 101, 1881
6. Making Symmetrical Designs
To achieve ½ turn (180°) rotational symmetry: Add shapes so the design balances opposite each other.
To achieve ¼ turn (90°) rotational symmetry: Place identical shapes in four directions (top, bottom, left, right).
Reflection symmetry in designs: Add lines of symmetry (vertical, horizontal, or diagonal) if both halves are identical.
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FAQs on Important Formulas: Symmetrical Designs - Mathematics (Maths Mela) Class 5 - New NCERT
| 1. What is the definition of symmetry in mathematics and nature? |  |
Ans. Symmetry refers to a balanced and proportionate similarity between two halves of an object or shape. In mathematics and nature, it represents the idea that a figure can be divided into parts that are arranged in a balanced way, often resulting in identical or similar patterns on either side of a dividing line or around a central point.
| 2. How does reflection symmetry differ from rotational symmetry? | |
Ans. Reflection symmetry, also known as line symmetry, occurs when one half of an object is a mirror image of the other half when divided by a line (the line of symmetry). On the other hand, rotational symmetry is present when an object can be rotated around a central point and still look the same at certain angles. For example, a butterfly exhibits reflection symmetry, while a star shape may display rotational symmetry.
| 3. Can you provide examples of shapes that exhibit both reflection and rotational symmetry? | |
Ans. Yes, several shapes exhibit both types of symmetry. A square is a common example, as it has four lines of reflection symmetry and can be rotated by 90 degrees around its center and still look the same. Similarly, a circle has infinite lines of reflection symmetry and exhibits rotational symmetry at any angle.
| 4. How is symmetry observed in numbers and digits? | |
Ans. Symmetry in numbers and digits can be observed through their shapes when written. For instance, the digit 0 has reflection symmetry because it looks the same when mirrored. Similarly, the digits 1 and 8 also exhibit reflection symmetry. Some numbers, like 2 and 5, do not have symmetry when reflected but can have rotational symmetry in specific contexts.
| 5. What are some methods for creating symmetrical designs in art or geometry? | |
Ans. To create symmetrical designs, one can use various methods such as folding paper along a line of symmetry to create mirror images, using geometry tools to ensure equal distances from a central point when drawing shapes, or utilizing digital design software that allows for mirroring and rotation features. Artists often employ these techniques to achieve balance and harmony in their compositions.
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like 1. Meaning of Symmetry, 2. Reflection Symmetry, 3. Rotational Symmetry, 4. Shapes with Both Reflection and Rotational Symmetry, 5. Symmetry in Digits & Numbers, 6. Making Symmetrical Designs and Important Formulas: Symmetrical Designs Example, for Class 5 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Important Formulas: Symmetrical Designs.
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