Symmetry: A Visual Presentation        

Line Symmetry A shape has line symmetry when one half of it is the mirror image of the other half. Symmetry exists all around us and many people see it as being a thing of beauty.

To be a line of symmetry, the shape must have two halves that match exactly. When you trace a heart onto a piece of folded paper, and then cut it out, the two half hearts make a whole heart. The two halves are symmetrical.

Which of these flags have a line of symmetry? United States of America NO Canada YES

What about these math symbols? Do they have symmetry? + - Yes Yes - x Yes Yes

Line Symmetry exists in nature but you may not have noticed.

At the beach, there are a variety of shells with line symmetry.

Under the sea there are also many symmetrical objects such as these crabs and this starfish. This type of symmetry is also called reflectional symmetry as the two parts reflect/match along each side of a dividing line ( or axis ).

Animals that have Line Symmetry Here are a few more great examples of mirror image in the animal kingdom.

REFLECTION IN WATER If an object is reflected in water, it is considered to have line symmetry along the waterline.

The Taj Mahal Symmetry exists in architecture all around the world.  The best known example of this is the Taj Mahal.

This photograph shows 2 lines of symmetry This photograph shows 2 lines of symmetry. One vertical, the other along the waterline. (Notice how the prayer towers, called minarets, are reflected in the water and side to side).

Shapes and Symmetry Do equilateral triangles have lines of symmetry? How many? Investigate by folding and make a conjecture!  

An equilateral triangle has 3 lines of symmetry.

Shapes and Symmetry Do squares have lines of symmetry? How many? Investigate by folding and make a conjecture!  

A square has 4 lines of symmetry.

Shapes and Symmetry Do regular pentagons have lines of symmetry? How many? Investigate by folding and make a conjecture!  

A regular pentagon has 5 lines of symmetry.

Shapes and Symmetry Do regular hexagons have lines of symmetry? How many? Investigate by folding and make a conjecture!  

A regular hexagon has 6 lines of symmetry .

Shapes and Symmetry Do trapezoids have lines of symmetry? How many would you guess? Investigate by folding and make a conjecture!  What would happen if the trapezoid was not isosceles?

An isosceles trapezoid has 1 line of symmetry.

Shapes and Symmetry Do parallelograms have lines of symmetry? How many would you guess? Investigate by folding and make a conjecture!  What would happen if the parallelogram was a rhombus?

    A parallelogram has no lines of symmetry, but a rhombus has 2 lines of symmetry.

A B C D E FG H I J K L M N O P Q R S T U V W X Y Z You can look to see if your name has symmetrical letters in it too! A B C D E FG H I J K L M N O P Q R S T U V W X Y Z Infinite number