Lines of symmetry

Your book, Maths Mela (Chapter 11), starts with an ink design. Fold a sheet of paper in half and open it. Drop some water colours on the fold. Close the sheet and press it, then open it again. The colour has spread to both sides, and the two halves match exactly!

A design like this is symmetrical. The line that divides it into two matching halves is called the line of symmetry. In the ink design, the line of symmetry is the fold. If you fold the paper along that line again, one half sits exactly on top of the other.

Next, the book makes a paper airplane. First you fold the sheet in half, down the middle, and open it. Then the top corners are folded in to the centre fold, making a pointed nose, and so on. At each of these steps the shape is symmetrical about the centre fold: the left side matches the right side.

When you unfold the finished plane (Fig. 8 in the book), the sheet has many creases fanning out from the middle of the top edge. It has 1 line of symmetry, straight down the middle. Stand a mirror on that line, and the reflection of the right half looks just the same as the left half.