12/20/20151.6: motion in geometry expectations: g1.1.6: recognize euclidean geometry as an axiom...
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04/21/23 1.6: Motion in Geometry
1.6: Motion in GeometryExpectations:
G1.1.6: Recognize Euclidean geometry as an axiom system. Know the key axioms and understand the meaning of and
distinguish between undefined terms (e.g., point, line, and plane), axioms, definitions, and theorems.
G3.1.1: Define reflection, rotation, translation, and glide reflection and find the image of a figure under a given isometry.
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TransformationsTransformations: Any change to a figure
Rigid Transformations: Transformations that ______________________________________.
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Preimage and Image.The _______________ is the original figure
(before the transformation).
The ___________is the figure that results from the transformation.
04/21/23 1.6: Motion in Geometry
Examples
This is a general transformation.
preimage image
04/21/23 1.6: Motion in Geometry
Examples
preimage image
This is a general transformation.
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Three Rigid Transformations1. __________________: 2 dimensional slide.
2. __________________: A turn around a certain point (center of the rotation).
3. ________________: A flip over a line.
04/21/23 1.6: Motion in Geometry
Examples
preimage image
This is a rigid transformation called a _________ or a ________________.
04/21/23 1.6: Motion in Geometry
Examples
preimageimage
This is a rigid transformation called a ________ or a ________________.
04/21/23 1.6: Motion in Geometry
Examples
preimage image
This is a rigid transformation called a _______ or a ________________.
04/21/23 1.6: Motion in Geometry
Drawing a Translationa. Draw a figure, F, and a line, l, on a sheet of
paper.
b. Trace the figure and the line on a separate sheet of paper. Do not move this paper until told to do so. Label F.
04/21/23 1.6: Motion in Geometry
Drawing a Translationc. Slide your top paper so that the line
remains on top of itself.
d. Trace the original figure (F) onto its new location on the top sheet. Label F’.
e. F’ is the image of F under a translation.
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Drawing a Rotationa. Draw a figure, F, and a point, P, not on the
figure.
b. Trace and label F and P on a separate sheet of paper (do not move this paper yet).
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Drawing a Rotationc. Place the point of your pen or pencil on P
and hold down securely. Rotate the bottom paper.
d. Trace F at its new location on your paper. Label the new figure F’.
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Drawing a Rotatione. F’ is the image of F under a rotation about
P.
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Drawing the Reflection of a Pointa. Draw a line l and a point P not on the line.
b. Fold your paper along l. Mark the location of P through the paper. The new point is P’, the reflection image of P over l.
04/21/23 1.6: Motion in Geometry
d. What relationship exists between PP’ and l?
c. Draw and label the point of intersection of l and PP’ as point X.
Drawing the Reflection of a Point
Line l is the perpendicular bisector of PP’.
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Line of Reflection TheoremThe line of reflection is the ______________
____________ of the segment connecting a pre-image point to its corresponding image point.
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Reflecting a Triangle
a. Draw a triangle, F, and a line, l, on your paper. Make dark dots at each of the vertices.
b. Fold your paper over line l such that F is hidden and crease the paper.
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Reflecting a Trianglec. Through your paper, mark the locations of your vertices.
Then open the paper back up. The new locations of your triangle should be transferred to the other side of the line.
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Reflecting a Triangled. Connect the new vertices and label the
figure F’.
e. F’ is the image of F under a reflection over line l.
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Rigid TransformationsMake a conjecture about the pre-images and
images in the 3 rigid transformations.
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Rigid Transformation TheoremUnder a rigid transformation, the image is
______________ to the pre-image.
ACT PrepWhat is the smallest possible value for the product of 2 integers that differ by 7?
A. 8
B. 0
C. -6
D. -10
E. -12
04/21/23 1.6: Motion in Geometry
04/21/23 1.6: Motion in Geometry
Assignment: pages 55 – 57, # 11, 15, 18, 20, 22 - 31, 39, 40