Read it again any time, including while you work through the exercises.
Take a sheet of paper, fold it in two, cut out a shape and unfold: the two halves match perfectly! The fold line is called the axis of symmetry, and we say the figure is symmetric about this axis. Butterfly wings, your face, a drawn heart: symmetry is everywhere in nature.
The axis of symmetry acts like a mirror. Every point of the figure has its reflection on the other side: at the same distance from the axis, but facing it. If a point is 2 squares left of the axis, its mirror image is 2 squares right, at exactly the same height.
Symmetry is a very honest transformation: it never cheats on measurements. The reflection of a 5 cm segment measures 5 cm, the reflection of a right angle is a right angle. Only the orientation changes: the image is flipped, like your right hand becoming a left hand in the mirror.
Some figures have several axes of symmetry. The square has 4: two through the midpoints of the sides, two along the diagonals. The circle is the king of symmetry: every diameter is an axis! Ready to play mirror?
On a grid, point M is 3 squares left of the axis (a vertical line). Where do you place its mirror image M'?
- 1
distance de M à l'axe : 3 carreaux
I count the squares between M and the axis, going straight across, perpendicular to the axis: there are 3.
- 2
3 carreaux de l'autre côté
I cross the axis and count 3 squares on the other side, at the same height: the mirror sends the point straight across, at equal distance.
- 3
M' à 3 carreaux à droite
I place M' exactly there. M and M' are at the same distance from the axis, the golden rule of symmetry.
Result: M' is 3 squares right of the axis, at the same height as M.