Revision:Symmetry

TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > Symmetry

2D Symmetry

Line symmetry

If a shape has a line of symmetry, the line of symmetry will divide the shape into two equal parts, one half of which can be folded along the line of symmetry to fit exactly onto the other. Note, a rectangle has two (not four) lines of symmetry and a circle has an infinite number.

Rotation symmetry

If rotating a shape through a certain angle produces an identical shape, it has rotational symmetry. If the shape can be rotated 4 times before returning to its original shape (e.g. a square), it has rotational symmetry of order 4. An equilateral triangle has rotational symmetry of order 3 and a rectangle of order 2.

One way of fining the order of rotational symmetry is to turn the shape and count how many times it looks exactly the same as you pass it though one whole turn (360 degrees).

We say a shape does not have any rotational symmetry, or is not rotationally symmetric if it's order of rotation symmetry is 1. This is because is ill not look like itself at all until you turn it back round to its starting position.

For example:

A Triangle's order of rotation symmetry is 3.

A Square's order of rotation symmetry is 4.

3D Symmetry

Plane symmetry

Plane symmetry involves 3-D solids. Whereas flat shapes can have mirror lines the solids have plane symmetry.

Rotational symmetry

This is where you can rotate the shape into different positions that look exactly the same. If there's 1 position, its 1 order symmetry or can be called 'no order'.

Comments

Explain an give egs for 3d symmetry.

Create diagrams to illustrate some of the points here.

Add in some exam tips.