Symmetry | A

Question 1

Does a square have only one line of symmetry? Take a square piece of paper. By folding, find all its lines of symmetry.

Question diagram 1
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Solution
Understand the Question
  • A line of symmetry is a fold line that divides a shape into two identical halves that match each other exactly.
  • By folding a square sheet of paper along different directions (middle folds and corner-to-corner diagonal folds), we can determine whether both halves match and count the total number of lines of symmetry.

Step 1 · Vertical Fold (First Line)

Fold the square sheet of paper in half by matching the left edge to the right edge.Diagram 1

The two halves overlap completely. This vertical crease gives the first line of symmetry.

Therefore, a square has more than one line of symmetry.

Step 2 · Horizontal Fold (Second Line)

Unfold the paper and fold it in half horizontally by matching the top edge to the bottom edge.Diagram 2

The two halves match exactly. This horizontal crease gives the second line of symmetry.

Step 3 · First Diagonal Fold (Third Line)

Unfold the paper and fold it along one diagonal by matching one corner to its opposite corner.Diagram 3

The two triangular halves overlap perfectly. This crease gives the third line of symmetry.

Step 4 · Second Diagonal Fold (Fourth Line)

Unfold the paper and fold it along the other diagonal by matching the remaining two opposite corners.Diagram 4

The two halves overlap perfectly. This crease gives the fourth line of symmetry.

Step 5 · Count All Lines of Symmetry

Unfold the paper completely to view all the fold creases.Diagram 5

There are 44 distinct fold lines:

  • 11 vertical line of symmetry
  • 11 horizontal line of symmetry
  • 22 diagonal lines of symmetry
Answer

No, a square does not have only one line of symmetry. It has 44 lines of symmetry.

Common Mistakes
  • Missing Diagonal Symmetry: Forgetting that diagonal folds also divide a square into matching halves, confusing a square with a non-square rectangle (which has only 22 lines of symmetry).
  • Counting Symmetrical Halves instead of Lines: Counting the 88 triangular sections formed by the folds instead of the 44 straight lines passing through the center.

More questions in A

Q1

Does a square have only one line of symmetry? Take a square piece of paper. By folding, find all its lines of symmetry.

Q2

Ink Blot Devils

Take a piece of paper. Fold it in half. Open the paper and spill a few drops of ink (or paint) on one half.

Now press the halves together and then open the paper again.

  • What do you see?
  • Is the resulting figure symmetric?
  • If yes, where is the line of symmetry?
  • Is there any other line along which it can be folded to produce two identical parts?
  • Try making more such patterns.
Q3

Use thin rectangular coloured paper. Fold it several times and create some intricate patterns by cutting the paper, like the one shown here. Identify the lines of symmetry in the repeating design.

Q4

Trace and cut out a copy of this figure. By rotating the cutout over this figure determine its angles of rotation.

Q5

Game

Draw a 6×66 \times 6 grid. Two players take turns covering two adjacent squares by drawing a line. The line can be placed either way: horizontally or vertically. The lines cannot overlap. The game goes on till a player is not able to place any more lines. The player who is not able to place a line loses.

With what strategy can one play to win this game?

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