Illuminations: Reflect on This

# Reflect on This

 This lesson, adapted from an activity in Navigating through Geometry in Grades 9‑12, requires students to investigate reflections using hinged mirrors. With a kaleidoscope, students will examine the interior angles of regular polygons.

### Learning Objectives

 Students will: Use multiple reflections to create regular polygons Determine the relationship between the number of sides in a regular polygon and the measure of its central angles Examine the significance of congruent angles and their applications

### Materials

 Mirrors (about 10 cm × 12 cm) Tape Sheets of white and colored paper Protractors Straightedges Reflect On This Activity Sheet Reflections Activity Sheet

### Assessment Options

 Students should be able to transfer their discoveries from this lesson to application problems. To assess their level of understanding, distribute the Reflections activity sheet, and allow students to complete it as an in-class assignment or as homework. Discuss the answers to the activity sheet as a class.

### NCTM Standards and Expectations

 Geometry 9-12Use various representations to help understand the effects of simple transformations and their compositions. Understand and represent translations, reflections, rotations, and dilations of objects in the plane by using sketches, coordinates, vectors, function notation, and matrices. Draw and construct representations of two- and three-dimensional geometric objects using a variety of tools.

### References

 Day, Roger, Paul Kelley, Libby Krussel, Johnny W. Lott, and Jame Hirstein. Navigating through Geometry in Grades 9‑12. Reston, VA: NCTM. 2001.

2 periods

### Web Sites

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