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Topic 12 Classwork Assignment
Problem 1: Determine if the transformation is a rotation, a translation, a reflection or a glide reflection.
For the rotation, use an O to designate the center of rotation. For the reflection, use a black dotted
line to designate the line of reflection. For the translation, use a black arrow to designate the direction
and the distance of the translation. For the glide reflection, use a red dotted line to designate the line of
reflection and a black arrow to designate the direction.
(a)
(b)
Type of transformation:
(c)
Type of transformation:
(d)
Type of transformation:
Type of transformation:
Problem 2: For each pattern, identify the smallest angle of rotation and a center of rotation. Use a * to
designate a 60° rotation, a × to designate a 90° rotation, a ? to designate a 120° rotation, and a °
to designate a 180° rotation. For a rotation of a 0°, write No rotation.
(a)
(b)
Angle of Rotation:
(d)
(c)
Angle of Rotation:
Angle of Rotation:
(e)
Angle of Rotation:
Angle of Rotation:
Problem 3: Label all lines of reflection in the pattern. Use a black dotted line to designate the lines of
reflection of reflections and a red dotted line to designate the lines of reflection of glide reflections.
Topic 12
Symmetry in Geometry:
Transformations
Transformations
Transformations move a shape without making any changes to its shape or size.
The four geometric transformations that preserve symmetry are: rotations, translations,
reflections, and glide reflections.
A rotation turns a shape about a point through a particular angle.
A translation moves or slides a shape a particular distance in a particular direction.
A reflection flips a shape across a line of reflection to create a mirror image.
A glide reflection is a reflection across a line of reflection followed by a translation in
the direction of the line.
2
Rotations
A rotation turns a shape about a point through a particular angle. The point is called
the center of rotation, which in the general case, we will designate with an O. The
angle is called the angle of rotation, which we will measure in degrees and designate
with the symbol ?. We will use a protractor to measure ?.
3
Rotations
To rotate a shape about a center of rotation through an angle of rotation, imagine a string
connects the center of rotation to a point on the shape. For a 40° rotation, we have:
? = 40°
center of
rotation
4
Rotations
Rotations through the angles 0°, 60°, 90°, 120°, and 180° often preserve symmetry.
5
0° Rotations
A rotation of 0° means no rotation.
No rotation.
6
60° Rotations
We use a *
to designate a
60° rotation.
*
7
90° Rotations
We use a ×
to designate a
90° rotation.
×
8
120° Rotations
We use a ?
to designate a
120° rotation.
?
9
180° Rotations
We use a ° to
designate a 180°
rotation.
180° Rotation
°
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Example: Rotations
For each pattern, identify the smallest angle of rotation and a center of rotation. Use a *
to designate a 60° rotation, a × to designate a 90° rotation, a ? to designate a 120°
rotation, and a ° to designate a 180° rotation. For a rotation of a 0°, write No rotation.
Solution:
°
(a)
(b)
(c)
?
×
(d)
180° rotation
(e)
120° rotation
90° rotation
*
0° rotation
60° rotation
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Reflections, Translations, Glide Reflections
A reflection flips a shape across a line of reflection to create a mirror image. We will
designate the line of reflection of a reflection with a black dotted line.
line of
reflection
12
Reflections, Translations, Glide Reflections
A translation moves or slides a shape a particular distance in a particular direction.
We will designate the direction of a translation with a black arrow.
13
Reflections, Translations, Glide Reflections
A glide reflection is a translation followed by a reflection about a plane parallel to
the direction of the translation. We will designate the line of reflection of a glide
reflection with a red dotted line and the direction of a glide reflection with a black
arrow.
14
Example: Reflections, Translations, Glide Reflections
Identify which pattern has reflections and which pattern has glide reflections. Label all
lines of reflection. Use a black dotted line to designate the lines of reflection of
reflections and a red dotted line to designate the lines of reflection of glide reflections.
Solution:
(a)
(b)
glide reflections
reflections
15