# Activities

• • • ##### Subject Area

• Math: Geometry: Transformational Geometry

• ##### Author 9-12

60 Minutes

• ##### Device
• TI-83 Plus Family
• TI-84 Plus
• TI-84 Plus Silver Edition
• ##### Software

Cabri Geometry™
TI Connect™

• ##### Accessories

TI Connectivity Cable

• ##### Other Materials
This is Activity 12 from the EXPLORATIONS Book:
Exploring The Basics Of Geometry With Cabri

Transformation

#### Activity Overview

In this activity, students study different types of transformations.

#### Before the Activity

Install the Cabri™: Jr. App on the students' graphing calculators using one of these two methods:

• TI-Connect™,  a TI Connectivity Cable, and the Unit-to-Unit Link Cable
• TI-Navigator™  "send to class" feature
• See the attached PDF file for detailed instructions for this activity
• Print pages 49 - 52 from the attached PDF file for your class
• #### During the Activity

Distribute the pages to the class.

Translation:

• Construct an asymmetrical polygon
• Draw a line to the right of the polygon
• Reflect the polygon across the line
• Draw a line to the right of the second polygon, and parallel to the first line
• Reflect the second polygon across the line
• Identify that when an image is reflected over two parallel lines, the transformation is a translation
• Measure the distance between the parallel lines
• Measure the distance between a vertex of the original polygon (pre-image) and its corresponding vertex in the final polygon (image)
• Measure the distance between one other vertex and its corresponding vertex in the third polygon
• Observe that the distance between the parallel lines is half the distance of the image and pre-image

• Rotation:
• Draw and label a line CD
• Construct a point A on line CD and draw a line through A
• Mark a point B on the line through A
• Construct an asymmetrical polygon in the interior of angle DAB and reflect it across line AB
• Reflect the new polygon over line AC
• Identify that when an image is reflected over two intersecting lines, the transformation is a rotation
• Measure angle BAC
• Measure the angle between the corresponding parts of the pre-image and image
• Note that the angle from the pre-image to image is twice the angle of rotation
• Drag line AC to change the angle between the two intersecting lines
• Identify that the relationship between the angle from the pre-image to image and the angle of rotation, does not hold true for an obtuse angle because the angle is being read from the other direction
• #### After the Activity

Review student results:

• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary