This presentation is the property of its rightful owner.
1 / 24

# GBK Geometry PowerPoint PPT Presentation

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.

GBK Geometry

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.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

## 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.

1

2

3

### 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.

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!