12/20/20151.6: Motion in Geometry Expectations: G1.1.6: Recognize Euclidean geometry as an axiom system. Know the key axioms and understand the meaning.

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Presentation transcript:

12/20/ : Motion in Geometry Expectations: 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.

12/20/ : Motion in Geometry Transformations Transformations: Any change to a figure Rigid Transformations: Transformations that ______________________________________.

12/20/ : Motion in Geometry Preimage and Image. The _______________ is the original figure (before the transformation). The ___________is the figure that results from the transformation.

12/20/ : Motion in Geometry Examples This is a general transformation. preimage image

12/20/ : Motion in Geometry Examples preimage image This is a general transformation.

12/20/ : Motion in Geometry Three Rigid Transformations 1. __________________: 2 dimensional slide. 2. __________________: A turn around a certain point (center of the rotation). 3. ________________: A flip over a line.

12/20/ : Motion in Geometry Examples preimage image This is a rigid transformation called a _________ or a ________________.

12/20/ : Motion in Geometry Examples preimageimage This is a rigid transformation called a ________ or a ________________.

12/20/ : Motion in Geometry Examples preimageimage This is a rigid transformation called a _______ or a ________________.

12/20/ : Motion in Geometry Drawing a Translation a. 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.

12/20/ : Motion in Geometry Drawing a Translation c. 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.

12/20/ : Motion in Geometry Drawing a Rotation a. 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).

12/20/ : Motion in Geometry Drawing a Rotation c. 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’.

12/20/ : Motion in Geometry Drawing a Rotation e. F’ is the image of F under a rotation about P.

12/20/ : Motion in Geometry Drawing the Reflection of a Point a. 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.

12/20/ : 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’.

12/20/ : Motion in Geometry Line of Reflection Theorem The line of reflection is the ______________ ____________ of the segment connecting a pre-image point to its corresponding image point.

12/20/ : Motion in Geometry 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.

12/20/ : Motion in Geometry Reflecting a Triangle c. 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.

12/20/ : Motion in Geometry Reflecting a Triangle d. Connect the new vertices and label the figure F’. e. F’ is the image of F under a reflection over line l.

12/20/ : Motion in Geometry Rigid Transformations Make a conjecture about the pre-images and images in the 3 rigid transformations.

12/20/ : Motion in Geometry Rigid Transformation Theorem Under a rigid transformation, the image is ______________ to the pre-image.

ACT Prep What is the smallest possible value for the product of 2 integers that differ by 7? A. 8 B. 0 C. -6 D. -10 E /20/ : Motion in Geometry

12/20/2015 Assignment: pages 55 – 57, # 11, 15, 18, 20, , 39, 40