### Geometry

```Geometry
Chapter 7
Benedict
Vocabulary
Image- Figures can be reflected, rotated,
or translated to produce new figures.
Preimage- The original figure of an
image.
Transformation- Moving the pre-image
onto the image.
Vocabulary
Image- Figures can be reflected, rotated,
or translated to produce new figures.
Preimage- The original figure of an
image.
Transformation- Moving the pre-image
onto the image.
Vocabulary
Types of Transformations
Translation
Practice
Draw a figure below and use the three
basic transformations to redraw your
original shape.
Vocabulary
Reflections- A transformation that uses a line
that acts like a mirror with an image
reflected in the line.
Line of Reflection- the mirror line.
Reflection Theorem- A reflection is isometry.
Line of Symmetry- The figure can be mapped
onto itself by a reflection in the line.
Practice
Label the line of reflection and the line of symmetry.
Vocabulary
Rotation- a transformation in which the figure
is turned about a fixed point.
Center of Rotation- the fixed point, about
which the figure moves.
Angle of Rotation- The point and its image for
an angle.
Rotation Theorem- A rotation is an isometry.
Practice
Label the center and angle of rotation.
Vocabulary
Rotational Symmetry- If the figure can
be mapped onto itself by a rotation of
180° or less.
Theorem 7.3- If lines k and m intersect at
point P, then a reflection in k followed
by a reflection in m is a rotation about
point P.
Vocabulary
Translation- A transformation that maps
every to points P and Q in the plane to
points P’ and Q’, so that the following
properties are true.
• PP’ = QQ’
• PP’ is parallel to QQ’ or PP’ and QQ’ are
collinear
Translation Theorem- A translation is an
isometry.
Practice
Label the points and lines in the drawing.
Vocabulary
Vector- A quantity that has both direction and
magnitude, or size, and is represented by an
arrow drawn between two points.
Initial Point- Starting point of a vector.
Terminal Point- Ending point of a vector.
Component Form- A vector that combines
vertical and horizontal components.
Practice
Below draw a picture of a vector, label the
initial and terminal point:
Vocabulary
Glide Reflection- A transformation in which
every point P is mapped onto a point P” by
the following steps.
1. A translation maps P onto P’.
2. A reflection in a line k parallel to the
direction of the translation maps P’ onto P”.
Composition- When two or more
transformations are combine to produce a
single transformation.
Practice
glide reflection below:
Vocabulary
Composition Theorem- The composition of
two (or more) isometries is an isometry.
Frieze Pattern/Border Pattern- A pattern
that extends to the left and right in such a
way that the pattern can be mapped onto
itself by a horizontal translation.
Practice
Draw the following Frieze Patterns below:
•
•
•
•
•
Translation