Order of rotational symmetry of an equilateral triangle

Step by step

The question

Question: what is the order of rotational symmetry of an equilateral triangle?

1 Mark a corner

Put a dot on one corner, so we can follow it.

Then turn the shape about its center.

2 Turn and count

After a third of a turn, it fits on itself again.

That is 1.

After two thirds of a turn, it fits on itself again.

That is 2.

One more turn: the dot is back at the start.

That is 3.

3 The order

It fits 3 times in one full turn.

So the order is 3.

Careful!

The start and the full turn are the same place.

Count it once.

4 Check

Let's check.

One full turn is 360 degrees.

Shared by 3, each turn is 120°.

3 turns of 120 degrees make 360 degrees: one full turn.

Right!

Let's look back.

First: mark a corner.

Then: turn and count.

Then: the order.

Last: check.