Reflectional and Rotational Symmetry (Unit 5)

" s y m m e t r y "

Shapes can have line symmetry and rotational symmetry.

Reflectional
and Rotational Symmetry

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Learning Target and Success Criteria

Learning Target

Success Criteria

❏

I can identify line
symmetries in two
dimensional figures

❏

I can identify rotational
symmetries in two
dimensional figures

❏

I will look for lines of
symmetry in a figure

❏

I will see if the figure lines
up with itself after the
symmetry is performed

❏

I will check for rotational
symmetry in the figure

Line Symmetry

Some of these shapes have one or more lines of symmetry.

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Real World Example

State whether the object appears to have line symmetry.

Multiple Select

Which of these figures have line symmetry?

Lines of Symmetry

• The line of symmetry can be defined as the axis or imaginary line that passes through the center of the shape or object.

• It divides it into identical halves.

Multiple Choice

How many lines of symmetry does this shape have?

• 0
• 1
• 2
• 4

Multiple Choice

How many lines of symmetry do this figure have?

• 0

• 1

• 2

• 4

When the polygon is regular, the Greek Prefixes
below tell the number of lines of symmetry.

• Pentagon - 5 sides and lines of symmetry

• Hexagon - 6 sides and lines of symmetry

• Heptagon - 7 sides and lines of symmetry

• Octagon - 8 sides and lines of symmetry

• Nonagon - 9 sides and lines of symmetry

• Decagon - 10 sides and lines of symmetry

Let's see how these lines of symmetry work with transformations.

The lines of symmetry are the lines of reflection that maps a figure onto itself.

Multiple Choice

How many lines of symmetry does this Rhombus have?

• 0

• 1

• 2

• 4

Rhombus

(Diamond) Another common figure which only has 2 lines of symmetry. (Not Regular)

Multiple Choice

How many lines of symmetry do a hexagon have?

• 5 lines

• 6 lines

• 7 lines

• 8 lines

What Are Regular Polygons?

• A regular polygon is an n-sided polygon in which the sides are all the same length and are symmetrically placed about a common center. (Also Equal interior angles)

• Equilateral Triangle and Square

• Regular: Pentagon, Hexagon, Heptagon, Octagon, Nonagon, Decagon, .......

Multiple Select

Select two that will map the following figure onto itself.

• x axis

• y axis

• y = 1

• x = 2

Multiple Select

Select two that will map the following figure onto itself.

• y = -2

• y = x

• y axis

• x = 4

• x = -2

Rotational Symmetry

How many times do you have to turn this shape to get back to where you started?

Rotational Symmetry

If a figure is rotated around a centre point and it still appears exactly as it did before the rotation, it is said to have rotational symmetry.

In the image is common polygons with either no rotational symmetry or 180 degrees of rotational symmetry.

Rotational Symmetry

How many degrees of rotational symmetry does each shape have?

Regular Polygons with Rotational Symmetry

• The rotational symmetry of a regular polygon is determined by the exterior angle of the regular polygon.

• Exterior angle is the minimum degree of rotation.

  Exterior Angle =

• 360 divided by # of sides

Minimum Degree for Regular Polygons

• Square - 4 sides 90^o minimum rotation 360/4 = 90

• Hexagon - 6 sides 60^o minimum rotation 360/6 = 60

• Heptagon - 7 sides 51.4^o minimum rotation 360/7 = 51.4

Multiple Choice

What is the order of rotational symmetry?

• 3

• 5

• 8

• 10

Multiple Choice

How many degrees of rotational symmetry does this figure have?

• 25

• 45

• 90

• 120

Multiple Choice

What is the order of rotation in the recycling symbol?

• 1
• 2
• 3
• 1,000

Multiple Choice

What is the order and angle of rotation (magnitude) of the flag?

• Order 2, 180 degrees

• Order 4, 90 degrees

• Order 3, 120 degrees

• Order 1, 360 degrees

Fill in the Blank

What is the minimum degree of rotation for a pentagon? (Just type the number of the degree)

Fill in the Blank

What is the minimum degree of rotation for a octagon? (Just type the number of the degree)

Multiple Select

Select two below that maps the following figure onto itself.

• 180^o degree rotation about point (0,3)

• 72^o degree rotation about point (0,3)

• 144^o degree rotation about point (0,3)

• 45^o degree rotation about point (0,3)

Multiple Select

Select all that apply.

• 180 degree rotation about point (0,1)

• A reflection about the line y = 1

• A reflection about y axis

• A reflection about the x axis

• 90 degree rotation about point (0,1)