5.2/5.4 Define and Apply Rotations + Symmetry

​5.2/5.4
Define and Apply Rotations
+ Symmetry

By Matthew T Eddleman

Definitions

rotation (turn) - a rigid motion that turns a figure through an angle of rotation about a point, such that each point and its image are the same distance from the point

angle of rotation - the angle in which a figure is turned around a point

center of rotation - the point that will be rotated around

SPECIAL NOTE: Unless otherwise stated, we always rotate counter-clockwise

Multiple Select

Select each transformation that appears to be a rotation.

Rules (push play)

Rotate a Figure Onto Itself

Regular polygons can be rotated so that the image of the figure looks exactly like the preimage. The angles of rotation that map a regular polygon to itself depend on the number of sides of the polygon. You can use the formula of 360°/n,  where n represents the number of sides to determine the angle of rotation.

Open Ended

What is the smallest angle of rotation that maps an equilateral triangle onto itself?

Open Ended

What is the smallest angle of rotation that maps a square onto itself?

Line Symmetry

Definitions

symmetry - a transformation that maps the figure to itself

line symmetry - a property of a figure that means it can be reflected across a line so that the image coincides with the preimage

line of symmetry - a line that divides the figure into two congruent reflected halves (also called the axis of symmetry)

Open Ended

Does a figure exist that has an infinite number of lines of symmetry? What would that figure be?

Dropdown

How many lines of symmetry does the figure have?​

Select answer

​ ​

Dropdown

How many lines of symmetry does the figure have?​

Select answer

​ ​

Dropdown

How many lines of symmetry does the figure have?​

Select answer

​ ​

Dropdown

How many lines of symmetry does the figure have?​

Select answer

​ ​

Draw

On the last question, you determined that a rectangle has only 2 lines of symmetry.  Is it possible for a rectangle to have 4 lines of symmetry? 

Explain why or why not. 

Use a diagram to support your answer if needed.

Rotational
Symmetry

Definitions

rotational symmetry - a property of a figure that can be rotated about a point by an angle less than 360° so that the image coincides with the preimage (also called radial symmetry)

angle of rotational symmetry - the smallest angle of rotation that maps a figure to itself

​Why can't an angle of rotational symmetry be 0°? Why can't it be greater than 180°?

• .A 0° rotation doesn’t count because that’s just the figure sitting in its original position — nothing has actually happened.

• Rotational symmetry is always measured by the smallest positive angle that maps the figure onto itself.

• If a figure has symmetry at, say, 270°, then it also has symmetry at 90° (since 270° = 360° – 90°). The 90° is smaller and is the one we use.

Open Ended

Tell whether the figure has line and/or rotational symmetry. Give the number of lines and/or the the angle of rotational symmetry.

Open Ended

Tell whether the figure has line and/or rotational symmetry. Give the number of lines and/or the the angle of rotational symmetry.

Open Ended

Tell whether the figure has line and/or rotational symmetry. Give the number of lines and/or the the angle of rotational symmetry.

Open Ended

Tell whether the figure has line and/or rotational symmetry. Give the number of lines and/or the the angle of rotational symmetry.

Recall from earlier in this lesson that a regular polygon has rotational symmetry and that you can find the angle of rotation by taking 360°/n, where n represents the number of sides. Take a look at the chart on the next slide to see the patterns associated with regular polygons and their different types of symmetry.

Open Ended

How many lines of symmetry would a regular hexagon have? What would be the angle of rotational symmetry?

Open Ended

How many lines of symmetry would a regular decagon have? What would be the angle of rotational symmetry?