Reflectional and Rotational Symmetry

Reflectional and Rotational Symmetry

​CO: I will identify and distinguish between reflectional and rotational symmetry in a plane figure.

LO: I will be able to discuss the differences between reflectional and rotational symmetry in a plane figure.

EQ: How can I identify reflectional and rotational symmetries in 2D and 3D figures?

Today's Lesson

• Connection to our Transformations

• Lesson Symmetry - What is Reflectional and Rotational Symmetry

• CYU - Reflectional and Rotational Symmetry

• Reflection

How is symmetry connected to our transformations?

​Look at this question. One transformation that would carry the rhombus onto itself is a reflection. Another one is a rotation. Can you find the line(s) of reflection and angle of rotation?

Multiple Select

Select all that apply

• A reflection with respect to y = 1

• A reflection with respect to the y axis

• A rotation about point (0,1) 180 degrees

• A rotation about point (0,1) 90 degrees

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 the picture have? (Rectangle)

• 0 lines of symmetry
• 1 line of symmetry
• 2 lines of symmetry
• 4 lines of symmetry

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

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)

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 Choice

How many lines of symmetry do a hexagon have?

• 5 lines

• 6 lines

• 7 lines

• 8 lines

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 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

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.

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

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)

Fill in the Blank

What is the minimum degree of rotation for a decagon (10-sides)? (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 Choice

Determine whether the figure has line symmetry, rotational symmetry, both, or neither.

• Rotational

• Line

• Both

• Neither

Open Ended

After going through this lesson, which type of problem(s) do you feel like you can do well? Explain.

Open Ended

After going through this lesson, which type of problem(s) do you feel like you are still struggling with? Explain.