Original notes — ready
Chapter 10: Symmetrical Designs
CBSE (NCERT, English Medium) • Class 5 • Mathematics • Book: Math Mela
Symmetrical Designs — EG's own notes, in simple words
Book: Math Mela (CBSE, Class 5) | Chapter 10 | Medium: English
Diagram (labels are printed on the image): A butterfly, a folded square and a rangoli. A general teaching picture about symmetry.
A symmetrical rangoli. A general picture about balanced designs.
What the chapter is about
A shape is symmetrical when it can be folded into two matching halves. The fold line is called the line of symmetry. Your face, a butterfly, and the letter A all have lines of symmetry.
Some shapes have many lines of symmetry: a square has 4, a circle has countless lines, and a rectangle has 2. Some shapes, like a scalene triangle, have none.
Symmetry makes designs beautiful — rangoli, tiles, flowers and buildings all use it. Artists and architects use symmetry to make things look balanced.
Symmetry is also found in nature and in our own bodies. Leaves, flowers, butterflies and your own face all show matching halves. Artists copy nature's balance because our eyes find balanced shapes pleasing.
What you should learn
Test symmetry by folding: if both halves match exactly, the fold is a line of symmetry. If they do not match, it is not.
Key Terms
- Symmetry — When two halves of a shape match exactly.
- Line of symmetry — The fold line dividing matching halves.
- Mirror image — The reflection of a shape, like in a mirror.
- Balanced — Looking equal and steady on both sides.
- Design — A decorative pattern.
- Mirror — A surface that reflects an image; the reflection is a mirror image.
Remember
- Symmetry = two matching halves.
- Square: 4 lines; rectangle: 2 lines; circle: countless.
- Fold test: halves must match exactly.
- Rangoli and tiles use symmetry.
Exam Tip / Common Mistake
Common mistake: saying a rectangle has 4 lines of symmetry. Its diagonals do NOT give matching halves — only the two mid-lines work.
Chart / Table: Lines of symmetry
| Shape | Lines of symmetry |
|---|---|
| Square | 4 |
| Rectangle | 2 |
| Equilateral triangle | 3 |
| Circle | Countless |
| Letter A | 1 |
Think and try
Write the capital letters A, B, C, D, E on paper. Fold each letter in your mind: which ones have a line of symmetry, and which do not? Compare your answers with a friend's.
Practice set — try it yourself
- How many lines of symmetry does a square have?
Hint: Fold it in your mind. - Does the letter B have a line of symmetry?
Hint: Think about top-bottom halves. - Draw a butterfly and mark its line of symmetry.
Hint: The body is the fold line. - Name one symmetrical and one non-symmetrical object at home.
Hint: Test by folding. - How many lines of symmetry does a circle have?
Hint: Think about folding through the centre in any direction.
How to use this page: Read the summary, say the Key Terms in your own words, then try the practice set without looking. Ask your teacher or parent to check your answers.