Unit 4, Activity 1, Vocabulary Self-Awareness
Word/Phrase
+

–
Definition/Rule
Example
transformation
pre-image
image
rigid transformation
(rigid motion)
non-rigid
transformation
(non-rigid motion)
orientation
isometry
reflection
line of reflection
translation
rotation
center of rotation
Blackline Masters, Geometry
Page 4-1
Unit 4, Activity 1, Vocabulary Self-Awareness
degree of rotation
clockwise
counterclockwise
dilation
center of dilation
scale factor
similarity
transformation
composite
transformation
glide reflection
Procedure:
1. Examine the list of words/phrases in the first column.
2. Put a + next to each word/phrase you know well and for which you can write an accurate
example and definition. Your definition and example must relate to this unit of study.
3. Place a  next to any words/phrases for which you can write either a definition or an
example, but not both.
4. Put a – next to words/phrases that are new to you.
This chart will be used throughout the unit. As your understanding of the concepts listed
changes, you will revise the chart. By the end of the unit, you should have all plus signs. Because
you will be revising this chart, write in pencil.
Blackline Masters, Geometry
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Unit 4, Activity 1, Vocabulary Self-Awareness with Answers
Word/Phrase
+

transformation
–
Definition/Rule
A correspondence between two
sets of points such that each
point in the pre-image has a
unique image and that each
point in the image has exactly
one pre-image; a change in
size, orientation, or position of
a figure in space.
pre-image
The original object that is to
be transformed.
image
The “copy” of the object that
has been transformed.
rigid
transformation
(rigid motion)
non-rigid
transformation
(non-rigid
motion)
orientation
isometry
reflection
line of reflection
Blackline Masters, Geometry
Example
A transformation that
preserves measurements of
segments and angles; also
called an isometry (see below).
A transformation that does not
preserve measures of segments
and angles; the shape of the
pre-image may not be
preserved either.
The location (position and
angle) of an object in space in
relation to a set of reference
axes.
A transformation that
preserves measurements and
more specifically distances
between points; a
transformation that preserves
distances is also bound to
preserve angle measures; a
congruence transformation.
A transformation in which
each point in the pre-image
has an image that is the same
distance from the line of
reflection (see below). For a
point on the line of reflection,
the image is itself; aka “flip.”
The perpendicular bisector of
the segment joining each point
(pre-image) and its image.
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Unit 4, Activity 1, Vocabulary Self-Awareness with Answers
translation
rotation
center of rotation
angle (degree) of
rotation
clockwise
counterclockwise
dilation
center of dilation
scale factor
Blackline Masters, Geometry
A transformation which moves
an object a fixed distance in a
fixed direction; a composite of
two reflections over parallel
lines; aka slide.
A transformation that turns a
figure about a fixed point
called the center of rotation; a
composite of two reflections
over intersecting lines; aka
“turn.”
A fixed point about which a
figure is rotated; the point
where two intersecting lines of
rotation meet??
Rays drawn from the center of
rotation to a point on the preimage and its image form the
angle of rotation (measured in
degrees).
Rotation of an object to the
right indicated by a negative
angle of rotation.
Rotation of an object to the left
indicated by a positive angle of
rotation.
A transformation that produces
an image that is the same
shape as the pre-image but is a
different size; a stretch or
shrink of the pre-image.
A fixed point in the plane
about which all points are
expanded (stretched) or
contracted (shrunk).
The ratio by which an object is
enlarged or reduced; if greater
than 1 the image is an
enlargement; if between 0 and
1 the dilation is a reduction; if
the scale factor equals 1, the
figures are congruent.
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Unit 4, Activity 1, Vocabulary Self-Awareness with Answers
similarity
transformation
composite
transformation
glide reflection
A transformation that is the
composite of dilations and/or
reflections; a non-rigid
transformation; the shape of
the pre-image is preserved but
the size is changed.
The result of two or more
successive transformations.
A type of composite
transformation where a figure
is reflected then translated.
Procedure:
1. Examine the list of words/phrases in the first column.
2. Put a + next to each word/phrase you know well and for which you can write an accurate
example and definition. Your definition and example must relate to this unit of study.
3. Place a  next to any words/phrases for which you can write either a definition or an
example, but not both.
4. Put a – next to words/phrases that are new to you.
This chart will be used throughout the unit. As your understanding of the concepts listed
changes, you will revise the chart. By the end of the unit, you should have all plus signs. Because
you will be revising this chart, write in pencil.
Blackline Masters, Geometry
Page 4-5
Unit 4, Activity 3, A Basic Look at Transformations
Trace the following polygons on the patty paper or tracing paper given to you.
Blackline Masters, Geometry
Page 4-6
Unit 4, Activity 4, What Are Transformations?
What Are Transformations?
When learning about transformations, one might first look at the parts of the word.
Transformation can be separated into the prefix trans- and the word formation. The prefix transmeans “changing thoroughly” and formation means “the act of giving or taking form, shape, or
existence.” Taken together, a transformation can be described as “the act of changing a form or
shape.” Specifically, in geometry, a transformation may change the position, orientation, or size
of a figure in the plane.
Look at the transformations below. The figure drawn with the solid lines is called the
pre-image, or the original object that is being transformed. The figure drawn with dashed lines is
called the image, or the “copy” of the object that has been transformed.
pre-image
image
image
pre-image
Figure 1
Figure 2
The most basic transformation is a reflection. A reflection can be easily described as a
“flip”, however, that is not the most accurate definition. A reflection is a transformation in which
each point in the pre-image has an image that is the same distance from the line of reflection.
The line of reflection is the perpendicular bisector of the segment joining each point on the preimage with its corresponding point on the image. Look at the example below. The image is
labeled A’B’C’D’ (read A prime, B prime, C prime, D prime—the use of the apostrophe on the
letter is universally accepted to show that a figure is the image of a transformation).
A’
A
D
D’
P
C
B
B’
C’
m
Figure 3
Line m is the line of reflection in the figure and P is the point where line m intersects the segment
joining A and A’. Using a ruler, measure the distance from A to A’. Now, measure the distance
from A to P and the distance from P to A’. You should notice that AP and PA’ are equal. Use a
protractor to measure the angles formed at P. You should see that the angles all measure 90
Blackline Masters, Geometry
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Unit 4, Activity 4, What Are Transformations?
degrees. How do those measurements relate to the definition of the line of reflection given
earlier?
Another basic transformation is a translation, or “slide.” When a translation is
performed, the pre-image is moved a fixed distance in a fixed direction. The directions for
performing a translation could state to move the pre-image 5 inches to the right in which each
point on the pre-image is moved 5 inches to the right of the location to form the image.
Translations can also be thought of as the composition of two reflections over parallel lines.
Look at the example below.
pre-image
image
m
n
Figure 4
Notice there are two reflections. Lines m and n are parallel. The resulting image has the same
orientation as the pre-image, but has been moved to the right by 10 cm. A question to think
about: does the distance of the translation have any relationship to the distance between the
parallel lines?
A third transformation is called a rotation. This transformation may also be referred to as
a turn. A rotation is a transformation that turns a figure about a fixed point, called the center of
rotation, through a fixed angle of rotation (measured in degrees). The path the figure follows
during the rotation would form a circle around the center of rotation if the figure were rotated
360 degrees. A rotation can be performed with any degree measure and can be considered a
clockwise rotation or a counterclockwise rotation. A clockwise rotation will turn a figure to
the right around the center of rotation while a counterclockwise rotation will turn a figure to the
left around the center of rotation. All positive degree measures are assumed to indicate a
counterclockwise rotation, while all negative degree measures are assumed to indicate a
clockwise rotation.
X
Figure 5
Blackline Masters, Geometry
Page 4-8
Unit 4, Activity 4, What Are Transformations?
In Figure 5 above, X is the center of rotation. The angle of rotation is formed by drawing a
segment from one point on the pre-image to the center of rotation then drawing the required
angle using the center of rotation (X) as the vertex. The angle used in this figure is 90° clockwise,
or -90°. Question to think about: What would happen to the image if the center of rotation was
moved but the angle of rotation remained the same?
A rotation can also be defined as a composite of two or more reflections over intersecting
lines. Consider the example below.
m
pre-image
n
image
Figure 6
The intersection of lines m and n becomes the center of rotation. These lines happen to be
perpendicular. Notice how the image has been rotated in a counterclockwise direction around the
center (point of intersection). How could you determine what the angle of rotation is for this
diagram? Go back to the definition of rotation discussed earlier for some ideas.
The three transformations discussed so far have one thing in common. If you look at all
of the images and compare them to their corresponding pre-images, you will notice that the
measures of the segments and angles have not changed (go ahead—measure them if you wish!).
Since the images have the same shape and are the same size as the pre-images, they are
congruent. Each of these transformations is called an isometry. An isometry is a transformation
that preserves measurements of segments and angles and therefore produces an image congruent
to its pre-image. A transformation that is an isometry is also sometimes referred to as a rigid
motion or rigid transformation.
In geometry, there is one more important transformation. A dilation is a transformation
that produces an image that is the same shape as the pre-image but is a different size. Sometimes
they are referred to as a stretch or shrink (also called an enlargement or reduction). Each dilation
is focused at the center of dilation, or a fixed point about which all points are enlarged or
reduced. How much the figure is enlarged or reduced depends upon the scale factor, the ratio by
which an object is enlarged or reduced. If the scale factor is greater than 1, the image is an
enlargement of the pre-image. If the scale factor is between 0 and 1, the image is a reduction of
the pre-image.
B’
B
A
C’
C
Figure 7
E
E’
Blackline Masters, Geometry
D
D’
Page 4-9
Unit 4, Activity 4, What Are Transformations?
In Figure 7 above, the center of dilation is A. The measure of segment AB’ is 2 times the measure
of segment AB. Therefore, the image A’B’C’D’E’ is an enlargement of the pre-image ABCDE,
and the scale factor is 2. Notice, the measures of the corresponding segments are not equal,
however the measures of the corresponding angles are (you can verify this by using your
protractor). Therefore, dilation is not an isometry. Dilation is a non-rigid transformation, or a
non-rigid motion. Because the corresponding angles have the same measure and the
corresponding sides are proportional, these figures are similar which means dilation is a
similarity transformation.
Blackline Masters, Geometry
Page 4-10