Question 3
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.
Folding and cutting paper creates patterns that are symmetrical.
Step 1 — Making the pattern
We start with a rectangular paper. We fold it in half vertically. We cut an oval shape near the fold. When we unfold the paper. We see two oval holes. These two holes form our design.
Step 2 — Identifying the vertical line of symmetry
Look at the final design in the diagram. Imagine a line going straight down the middle. This line passes between the two oval holes. If we fold along this vertical line. The left half matches the right half. This means the vertical line is a line of symmetry.
Step 3 — Identifying the horizontal line of symmetry
Now, imagine a line going straight across the middle. This line passes through the center of each oval. If we fold along this horizontal line. The top half matches the bottom half. So, the horizontal line is also a line of symmetry.
Answer
The design has two lines of symmetry. (i) One vertical line of symmetry, passing between the two oval holes. (ii) One horizontal line of symmetry, passing through the centers of the two oval holes.
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?