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.
We can find lines of symmetry by folding a square piece of paper.
Step 1 — First Line of Symmetry
Let us take a square piece of paper. We fold the paper exactly in half. We match the left edge to the right edge. This fold line is a line of symmetry. Look at the diagram, "Fold 1". This shows a vertical fold. So, a square has at least one line of symmetry. The answer to "Does a square have only one line of symmetry?" is No.
Step 2 — Second Line of Symmetry
We unfold the paper completely. We fold the paper exactly in half again. We match the top edge to the bottom edge. This fold line is another line of symmetry. Look at the diagram, "Fold 2". This shows a horizontal fold.
Step 3 — Third Line of Symmetry
We unfold the paper completely. We fold the paper along one diagonal. We match one corner to the opposite corner. This fold line is a third line of symmetry. Look at the diagram, "Fold 3".
Step 4 — Fourth Line of Symmetry
We unfold the paper completely. We fold the paper along the other diagonal. We match the remaining two opposite corners. This fold line is a fourth line of symmetry. Look at the diagram, "Fold 4".
Step 5 — Count All Lines of Symmetry
We unfold the paper completely. We can see all the fold lines. There are four distinct fold lines. These four lines are all lines of symmetry. The last image in the diagram shows all four lines.
Answer
(i) No, a square does not have only one line of symmetry. (ii) A square has four lines of symmetry.
More questions in A
Does a square have only one line of symmetry? Take a square piece of paper. By folding, find all its lines of symmetry.
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.
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.
Trace and cut out a copy of this figure. By rotating the cutout over this figure determine its angles of rotation.
Game
Draw a 6 by 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?