Symmetry:Symmetry:A Visual PresentationA Visual Presentation

Line SymmetryLine Symmetry A shape has line symmetry when one A shape has line symmetry when one

half of it is the mirror image of the half of it is the mirror image of the other half.other half.

Symmetry exists all around us and Symmetry exists all around us and many people see it as being a thing of many people see it as being a thing of beauty.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

Canada

What about these math symbols?What about these math symbols?Do they have symmetry?

Line Symmetry exists in Line Symmetry exists in nature but you may not nature but you may not

have noticed.have noticed.

At the  beach, there are At the  beach, there are a variety of shells with a variety of shells with

line symmetry. line symmetry.

Under the sea there are also Under the sea there are also many symmetrical objects many symmetrical objects

such as these crabssuch as these crabs

and this starfish.and this starfish.

Animals that have Line Animals that have Line SymmetrySymmetry

Here are a few more great examples of Here are a few more great examples of mirror image in the animal kingdom.mirror image in the animal kingdom.

REFLECTION IN WATERREFLECTION IN WATER

If an object is If an object is reflected in water, reflected in water, it is considered to it is considered to

have line have line symmetry along symmetry along the waterline.the waterline.

The Taj MahalThe Taj Mahal

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

This photograph shows 2 lines of This photograph shows 2 lines of symmetry. One vertical, the other along symmetry. One vertical, the other along

the waterline.the waterline.

(Notice how the prayer towers, called minarets, are reflected in the (Notice how the prayer towers, called minarets, are reflected in the water and side to side).water and side to side).

Shapes and SymmetryShapes and Symmetry

Do equilateral triangles have Do equilateral triangles have lines of symmetry? How lines of symmetry? How

many? Investigate by folding many? Investigate by folding and make a conjecture!   and make a conjecture!  

An equilateral triangle has 3 lines of An equilateral triangle has 3 lines of symmetry. symmetry. 

Shapes and SymmetryShapes and Symmetry

Do squares have lines of Do squares have lines of symmetry? How many? symmetry? How many?

Investigate by folding and Investigate by folding and make a conjecture!   make a conjecture!  

        A square has 4 lines of symmetry.  A square has 4 lines of symmetry. 

   

Shapes and SymmetryShapes and Symmetry

Do regular pentagons have Do regular pentagons have lines of symmetry? How lines of symmetry? How

many? Investigate by folding many? Investigate by folding and make a conjecture!   and make a conjecture!  

    A regular pentagon has 5 lines of A regular pentagon has 5 lines of symmetry.symmetry.

  

Shapes and SymmetryShapes and Symmetry

Do regular hexagons have Do regular hexagons have lines of symmetry? How lines of symmetry? How

many? Investigate by folding many? Investigate by folding and make a conjecture!   and make a conjecture!  

A regular hexagon has 6 lines of A regular hexagon has 6 lines of symmetry . symmetry .

Shapes and SymmetryShapes and Symmetry

Do trapezoids have lines of Do trapezoids have lines of symmetry? How many would symmetry? How many would

you guess? Investigate by you guess? Investigate by folding and make a folding and make a

conjecture!  What would conjecture!  What would happen if the trapezoid was happen if the trapezoid was

not isosceles?not isosceles?

        An isosceles trapezoid has 1 line of An isosceles trapezoid has 1 line of

symmetry.symmetry.

Shapes and SymmetryShapes and Symmetry

Do parallelograms have lines Do parallelograms have lines of symmetry? How many of symmetry? How many

would you guess? Investigate would you guess? Investigate by folding and make a by folding and make a

conjecture!  What would conjecture!  What would happen if the parallelogram happen if the parallelogram

was a rhombus?was a rhombus?

        A parallelogram has no lines of A parallelogram has no lines of

symmetry, but a rhombus has 2 lines symmetry, but a rhombus has 2 lines of symmetry.of symmetry.

You can look to see if your name has symmetrical letters in it too!

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