GBK Geometry. Jordan Johnson. Today’s plan. Greeting Hand in Problem Write-up Lesson: Isometries, Congruence, and Symmetry Study Guide Clean-up. On parallelograms. Roger Shepard, 1981. Isometries / Rigid Motions.
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
GBK Geometry Jordan Johnson
Today’s plan • Greeting • Hand in Problem Write-up • Lesson: Isometries, Congruence, and Symmetry • Study Guide • Clean-up
Isometries / Rigid Motions • A transformation is an isometry (or rigid motion) iff it preserves distances and angles.
Definitions • Transformations definition of congruence: • Two figures are congruent iff there is an isometry in which one is the image of the other.
Definition • A glide reflection is the composite of a translation and a reflection in a line parallel to the direction of the translation. • In other words: Reflect, then translate, or vice versa.
3-fold Rotational Symmetry Flag of the Isle of Man
Translational Symmetry Other neat examples: autologlyphs and ambigrams.
A Tale of Two Fats Saturated Unsaturated
Summary • Each isometry has an associated symmetry: • Reflection symmetry with respect to a line: • Figure coincides with its reflection image through the line • Rotation symmetry: • Figure coincides with its image when rotated less than 360° • n-fold symmetry, if the smallest such rotation is 360°⁄n • Translation symmetry: • Figure coincides with its translation image
Homework • Problem for final • Study guide • Any make-up portfolio work • Recommended review for Unit 5: • Proof problems: • Two reflections across parallel lines= translation perpendicular to the lines of reflection. • Prove that the 3 transformations are isometries. • Asgs #37-38.
Clean-up / Reminders • Pick up all trash / items. • Push in chairs (at front and back tables). • See you tomorrow!