Lines of symmetry

The figure below is a rectangle. How many lines of symmetry does it have? Try it first. Pause if you like. Imagine folding the rectangle. Do the two halves fit exactly? Will the halves fit when we fold from left to right? Fold it from left to right. The two halves fit exactly. This fold line is a line of symmetry. Open it again. Keep that line. Will they fit when we fold from top to bottom? Now fold it from top to bottom. The two halves fit exactly again. This is another line of symmetry. Open it, and keep this line too. Will they fit along this diagonal? What about a fold from this corner to the opposite corner? The halves have the same size, but they do not fit exactly. The long side of one does not match the short side of the other. This diagonal is not a line of symmetry. Open the rectangle again. What do you predict for the other diagonal? Try the other diagonal. The halves do not fit exactly this way either. Only the folds that fit exactly count. 1 line down the middle. 1 line across the middle. 1 plus 1 is 2. The rectangle has 2 lines of symmetry.

Some of the squares on the grid below are shaded. How many lines of symmetry does the shaded figure have? Try it first. Pause if you like. This time, the shaded squares must land on shaded squares. Will the halves fit when we fold from left to right? Fold the grid from left to right. These shaded squares land on squares that are not shaded. This fold does not fit. Open the grid again. Will they fit when we fold from top to bottom? Now fold it from top to bottom. The shaded squares do not match this way either. There are other folds to test. Will they fit along this diagonal? Fold from the top left corner to the bottom right corner. Every shaded square fits onto a shaded square. This diagonal is a line of symmetry. Open it, and keep that diagonal. What do you predict for the other diagonal? Now fold from the top right corner to the bottom left corner. Every shaded square fits again. This diagonal is a line of symmetry too. Open the grid to see both lines. 1 diagonal. And the other diagonal. 1 plus 1 is 2. The shaded figure has 2 lines of symmetry. A line of symmetry is a fold line where the two halves fit exactly.