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Table of Contents

P.4 An Introduction to Symmetry

P.5 Reflection/ Line Symmetry

P.6 Important Note On Reflection Symmetry

P.7 Rotational Symmetry

P.8 Order of Rotation

P.9 Stop & Think About Symmetry

P.10 Real World Examples

P.11 Brainstorm: Landmarks and Monuments

P.12-P.13 Practice Problems 

Definition: a rigid motion that gives an image that is the 

same shape as the original shape.

Uses: can be used in design, art, and science- more 

specifically when studying molecules.

Two Types of Symmetry:

1. Reflection

2. Rotational Symmetry

What does this mean?

It means that the object can be split 

into two parts, and each part would 

fit on top of the other part if the 

figure were folded on the reflection 

line.

Where can we find reflection 

symmetry in nature?

Identify where the line of symmetry 

goes on these three objects.

Important Note:

A given shape can have more than one 

reflection symmetry.

Refer to the following examples:

Definition: Rotational symmetry exists 

when an object can be rotated around a 

fixed point until it fits exactly on the 

space it originally occupied.

Refer to the example below: the object 

was rotated clockwise until it resumed 

its original position.

Rotational Symmetry: Order of Rotation

What does order of rotation mean?

Order of rotation refers to the number of positions that 

the object can be rotated to within 360 degrees. 

Check out the examples below!

Order 1 is not listed because every object has order 1 

rotational symmetry. If you rotate an object one time at 360 

degrees, it will always return to its original shape.

Still not sure? Check out this link!

https://www.youtube.com/watch?v=OC2e9PGYYN0

Stop and Think!

Is it possible for a shape to have both 

reflection/line symmetry and 

rotational symmetry? Before reading 

on, try to come up with some 

examples of when this may be 

applicable. 

The answer: Yes!

For example: Equilateral triangles, 

squares, regular (meaning all angles 

are equal and all side lengths are 

equal) pentagons, regular hexagons, 

etc.

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