It lies in the plane. Can you still rotate it?

Geometry Level 1

Find the order of rotational symmetry of the octagon given above.

1 2 4 8

3 solutions

Sandeep Bhardwaj
Aug 24, 2015

The point to be notice here is that the given octagon is not a regular one i.e. all the interior angles are not equal. Hence we can clearly say by the given figure (below) that it does not look the same after $45^\circ$ of rotation.

So It will take $90^\circ$ rotation to look the same. Hence it will look the same when rotated by $90^\circ$ , $180^\circ$ , $270^\circ$ and finally at $360^\circ$ .

Hence the order of the rotational symmetry of the given octagon is $4. \square$

enjoy!

Moderator note:

Simple standard approach.

I've updated the image so that it is more obvious that the octagon isn't regular.

Calvin Lin Staff - 5 years, 9 months ago

Keshav Ramesh
Feb 9, 2017

The figure is the same when rotated 90 degrees - and since 360/90=4, the order of rotational symmetry of this octagon is 4.

Gwen Roberts
Sep 13, 2015

4 lines of symmetry.

Moderator note:

Can you elaborate further? What are the 4 lines of symmetry? Why are there only 4?

Imagine the figure was a piece of paper. A fold that cuts it in half is a line of symmetry. When you make that fold, one half of the figure "covers" the other. I found exactly 4 folds like this: all contain the center point, vertical line, horizontal line, and the two diagonals of the square.

Gwen Roberts - 5 years, 9 months ago

It lies in the plane. Can you still rotate it?

3 solutions

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