Symmetries

Line Symmetry

According to the book "A Problem Solving Approach to Mathematics for Elementary School Teachers," mathematically a geometric figure has a line of symmetry (l) " if its own image under a refection in (l).
According to the website "Math is Fun" "line of symmetry is another name for reflection symmetry. One half is the reflection of the other half.
The "Line of Symmetry"  is the imaginary line where you could fold the image and have both halves match exactly."
In other words Line of symmetry is when a figure, shape object or anything that when cut in fact shows the same exact thing in both sides! For example:

All things that have symmetry can also have more than just one line of symmetry. For example,
 
How many lines of symmetry does the letter A have?


Only 1 line of symmetry because only the third A with the horizontal line represents the reflection of the other side.

But unlike a other figures have more than one line of symmetry. For example:


in fact there is one shape that its symmetry is infinite, can you guess which one??

If you guessed a circle then your right! A circle has infinite symmetry.


Rotational Symmetry

 According to the book "A Problem Solving Approach to Mathematics for Elementary School Teachers," a figure has rotational symmetry " when the traced figure can be rotated less that 360 degrees about some point so that it matches the original figure." Remember its important to note that the condition  less than 360 degrees is clear and necessary because if we were to turn a figure 360 degrees it will coincide with itself.


 

 The figures above all classify to rotational symmetry!!


Point Symmetry
 According to the book "A Problem Solving Approach to Mathematics for Elementary School Teachers," "any figure that has rotational symmetry is said to have point symmetry about the turn center. The examples below are examples of figures with point symmetry:




Fact: if a figure has point symmetry it has rotational symmetry.