Download Basic Rigid Motions

Basic Rigid Motions
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A motion that maps a line to a line, a ray to a ray, a segment to a segment, and an angle to an angle.
A basic rigid motion preserves lengths of segments.
A basic rigid motion preserves measures of angles.
A basic rigid motions are translations, reflections, and rotations of Transformational Geometry.
Basic rigid motion produces congruent figures.
Congruency is obtain through a sequence of basic rigid motions. Figures are said to be congruent if one or more translations, reflections, or
rotations can map one figure onto the other.
Translations
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Reflections
Corresponding segments in the image and
pre-image are the same length measurement;
i.e. corresponding sides are congruent in
length.
Corresponding angles in the image and preimage have the same degree measurement; i.e.
corresponding angles are congruent in degree.
Parallel lines in the pre-image remain parallel
lines in the image. The parallel lines have the
same slope.
The location of the pre-image is changed to
produce the image through a coordinate rule.
Congruent figures are produced in a different
location in the plane.
The motion begins with a pre-image and is
mapped to an image.
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Slide
Coordinate rule is specified by a figure, a
distance, and a direction; sometimes using a
vector.
Segments connecting corresponding vertices
are the same length.
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Orientation of the figure does not change.
Image has the same orientation as the preimage.
Segments connecting corresponding vertices
are parallel to each other.
Slopes of corresponding segments do not
change.
Rotations
Corresponding segments in the image and
pre-image are the same length measurement;
i.e. corresponding sides are congruent in
length.
Corresponding angles in the image and preimage have the same degree measurement; i.e.
corresponding angles are congruent in degree.
Parallel lines in the pre-image remain parallel
lines in the image. The parallel lines have the
same slope.
The location of the pre-image is changed to
produce the image through a coordinate rule.
Congruent figures are produced in a different
location in the plane.
The motion begins with a pre-image and is
mapped to an image.
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Flip
Coordinate rule is specified by a figure and a
line of reflection.
Segments connecting corresponding vertices
are perpendicularly bisected by the line of
reflection.
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Orientation of the figure does change.
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Segments connecting corresponding vertices
are parallel to each other.
Slopes of corresponding segments may
change.
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Corresponding segments in the image and
pre-image are the same length measurement;
i.e. corresponding sides are congruent in
length.
Corresponding angles in the image and preimage have the same degree measurement; i.e.
corresponding angles are congruent in degree.
Parallel lines in the pre-image remain parallel
lines in the image. The parallel lines have the
same slope.
The location of the pre-image is changed to
produce the image through a coordinate rule.
Congruent figures are produced in a different
location in the plane.
The motion begins with a pre-image and is
mapped to an image.
Turn
Coordinate rule is specified by a figure, a
direction, a center of rotation, and an angle of
rotation.
Corresponding image and pre-image vertices
lie on the same circle
Orientation of the figure does not change.
Image has the same orientation as the preimage.
Segments connecting corresponding vertices
are not parallel to each other.
Slopes of corresponding segments may
change.