Symmetries of Plane Figures

Beyond the Fold - Exploring Plane Symmetries

Activity 1

Draw a shape on a piece of paper. Then, cut it out.
Fold the shape into half.

Concept: This fold is a line of symmetry. If one side is a mirror image of the other, it is called bilateral symmetry. The line is called line symmetry / axis of symmetry. Activity 2

Draw a square on a piece of paper. Then, cut it out.
Place a pencil tip in the center of the square paper and perform a full rotation slowly.
How many times does the shape look exactly the same as the object before you arrive at the start?

Concept: This is called rotational symmetry. The number of times the shape remains the same direction as the object throughout a full rotation is the order (ref. applet below to visualise). *If a shape has only one rotational symmetry throughout a full turn, then it is not considered to have any rotational symmetry. Can you think of any shape that does not have a rotational symmetry? Symmetry operations consist of two operations:

Reflection - flipping over a line
Rotation - rotating around a fixed center point.

Visualise rotational symmetry

Symmetry Hunt

Activity 3

Analyse an equilateral triangle and a regular hexagon.
How many lines of symmetry and the order of rotational symmetry do each of the shape have?
Can a shape have rotational symmetry but no line symmetry?

Activity 4