Hinglish

Line of Symmetry

Class 6 Maths · Chapter 9: Symmetry · NCERT Ganita Prakash section 9.1

Learn

Meher drops a blob of paint on one half of a sheet of paper, folds the sheet down the middle and presses. When she opens it, a butterfly appears! The two halves are mirror images of each other.

A shape has symmetry if a line splits it into two halves that match exactly when folded. That fold line is a line of symmetry (or mirror line). Fold along it, and one half lands exactly on the other.

Some shapes have more than one. A square has 4: up-down, across, and the two diagonals. A rectangle has only 2. Try folding a rectangle along its diagonal: the halves don't land on each other!

A regular polygon (all sides equal and all angles equal) has as many lines of symmetry as it has sides: an equilateral triangle has 3, a regular pentagon 5, a regular hexagon 6.

And some shapes have no line of symmetry at all, like a triangle whose sides are all different, or a parallelogram (a slanted rectangle). No fold makes the halves match.

Look for symmetry around you: the letters A, H, M, T, U; a rangoli at a doorway; a leaf; the front of a temple or a mosque. Fold-and-cut paper chains and punched holes in a folded paper also come out symmetric.

Explore: complete each picture so the dashed line is a line of symmetry.

  1. Mirror the blue squares across the line.
  2. Now the mirror line goes across.
  3. Two mirror lines! Make the picture symmetric about both.

Explore: tap the lines of symmetry.

  1. Tap all the lines of symmetry of the square.
  2. Now the rectangle.
  3. And the regular hexagon.

Remember

  • A line of symmetry splits a shape into two halves that match exactly when folded.
  • Square 4, rectangle 2, regular polygon with n sides: n. Some shapes have none.

Quick check

How many lines of symmetry does a rectangle (that is not a square) have?

  1. 2
  2. 4
  3. 1
  4. 0
Answer

2. Up-down and across. The diagonals are not lines of symmetry of a rectangle.

Think about it

Gauri folds a square sheet in half, and then in half again the other way. She punches one hole near a corner and opens it. How many holes are there, and where?

One answer

4 holes. Each fold doubles them, and the two fold lines are lines of symmetry, so the holes sit in matching positions in all four quarters.

Practice

Practise with fresh questions at three levels (easy, medium, hard), some answered hands-on, with hints and worked answers. Get 4 of your last 5 right to finish the topic.