Reflectional and Rotational Symmetry (Unit 5 EOC Prep)

" s y m m e t r y "

Shapes can have line symmetry and rotational symmetry.

I have it when I can identify lines of symmetry and rotational symmetry and justify (explain) how a figure maps onto itself.

​Success Criteria

I will be able to identify linear and rotational symmetry so I can determine if and how a figure maps onto itself.

Learning Targets

Learning Target / Success Criteria
G.CO.A.2

Voabulary:
line of symmetry
reflectional symmetry
rotational symmetry
center of rotation
interor angles
exterior angle
order of rotational symmetry
regular polygon
irregular polygon
reflectional symmetry

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

• All sides equal length (equilateral)

• All interior angles equal (equiangular)

What Are Regular Polygons?

• All sides have equal lengths = Number of lines of symmetry

• All interior angles have equal measure

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

• Pentagon - 5 equal sides and lines of symmetry

• Hexagon - 6 equal sides and lines of symmetry

• Heptagon - 7 equal sides and lines of symmetry

• Octagon - 8 equal sides and lines of symmetry

• Nonagon - 9 equal sides and lines of symmetry

• Decagon - 10 equal sides and lines of symmetry

Multiple Choice

How many lines of symmetry does a hexagon have?

• 5 lines

• 6 lines

• 7 lines

• 8 lines

​IRREGULAR POLYGONS

Sides are different lengths
Interior angles are different measures

Multiple Choice

How many lines of symmetry does this Rhombus have?

• 0

• 1

• 2

• 4

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 are 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 equal sides 90^o minimum rotation 360/4 = 90

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

• Heptagon - 7 equal 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 Blanks

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

Fill in the Blanks

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

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 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

Are You EOC Ready?
Exit ticket (2 questions)

Multiple Select

Select two below that maps the following figure onto itself.

(0,3) is the center of rotation

• 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.

Which transformation would carry the rhombus onto itself?

• 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)