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Schooling · Class 6 · Mathematics · Symmetry · Chapter on a page

CBSE Class 6 · Mathematics · NCERT Ganita Prakash

Symmetry: chapter on a page

A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).

About the notes: Written by Shishya's AI on 26 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.

This note's current text has no applied fact-check on record.

Mind map

Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.

Mind map of Symmetry: Key ideas, Formulas and facts, Watch out forKey ideassymmetryline of symmetrySome shapes have only one line of…regular polygonReflection symmetryIn reflection, every point on one…Nature is full of symmetryFormulas and factsLine of symmetryequilateral trianglesquarerectanglecircleregular hexagonThe letters A, H, M, O, T, U, V, W…Watch out forThinking every rectangle has four…Drawing a line of symmetry that does…Believing all triangles have three…Placing the reflected point at the…Symmetry
The mind map as a list
  • Key ideas
    • symmetry
    • line of symmetry
    • Some shapes have only one line of…
    • regular polygon
    • Reflection symmetry
    • In reflection, every point on one…
    • Nature is full of symmetry
  • Formulas and facts
    • Line of symmetry
    • equilateral triangle
    • square
    • rectangle
    • circle
    • regular hexagon
    • The letters A, H, M, O, T, U, V, W…
  • Watch out for
    • Thinking every rectangle has four…
    • Drawing a line of symmetry that does…
    • Believing all triangles have three…
    • Placing the reflected point at the…

What this chapter is about

Symmetry is all around you. Look at a butterfly, a rangoli, or even your own face in the mirror. When one half of something looks exactly like the other half, we say it has symmetry. This chapter helps you see and understand this beautiful pattern in shapes.

Key ideas

  • A shape has symmetry when you can fold it along a line and both halves match exactly, like two perfect twins lying on top of each other.
  • A line of symmetry is the fold line that divides a shape into two matching halves.
  • Some shapes have only one line of symmetry (like the letter A), some have many (like a square has four), and some have none (like the letter R).
  • A regular polygon is a shape with all sides equal and all angles equal. A regular polygon with n sides has exactly n lines of symmetry.
  • Reflection symmetry means one half is the mirror image of the other half.
  • In reflection, every point on one side of the line has a matching point on the other side, at the same distance from the line.
  • Nature is full of symmetry: leaves, flowers, insects, and snowflakes often show symmetric patterns.

Formulas and facts to remember

  • Line of symmetry: A line that divides a shape into two parts that are mirror images of each other.
  • An equilateral triangle (all three sides equal) has exactly 3 lines of symmetry.
  • A square has exactly 4 lines of symmetry (two through opposite corners, two through midpoints of opposite sides).
  • A rectangle (not a square) has exactly 2 lines of symmetry (through midpoints of opposite sides only).
  • A circle has infinitely many lines of symmetry (any line through its centre is a line of symmetry).
  • A regular hexagon has 6 lines of symmetry.
  • The letters A, H, M, O, T, U, V, W, X, Y (in capital block form) have at least one vertical line of symmetry.

Common mistakes

  • Thinking every rectangle has four lines of symmetry → Only a square (a special rectangle) has four; a rectangle that is not a square has only two.
  • Drawing a line of symmetry that does not divide the shape into matching halves → Always check by imagining a fold; both sides must overlap perfectly.
  • Believing all triangles have three lines of symmetry → Only an equilateral triangle has three; an isosceles triangle has one, and a scalene triangle has none.
  • Placing the reflected point at the wrong distance from the line → The reflected point must be at the same distance from the line, just on the opposite side.

Quick revision

  • A line of symmetry divides a shape into two matching mirror halves.
  • Fold test: if both halves overlap exactly, the fold line is a line of symmetry.
  • More equal sides and equal angles usually mean more lines of symmetry.
  • A circle has endless lines of symmetry; a scalene triangle has none.
  • Reflection places the image at the same distance from the line, on the other side.