# Reflectional and Rotational Symmetry: Quadrilaterals and Regular Polygons

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## Objective

SWBAT describe rotations and reflections that carry a quadrilateral or regular polygon onto itself.

#### Big Idea

Students will further investigate reflectional and rotational symmetry, specifically in quadrilaterals and regular polygons, which is demonstrated using Geometer's Sketchpad.

## Do Now

7 minutes

As the students walk into the room, I hand them a small slip of paper with four pictures of elements from international flags. In the lesson, “Reflectional and Rotational Symmetry,” students looked at the flags and identified various symmetries. For this activity, students delve deeper into the symmetries of the shapes by viewing the elements as regular polygons and not just random shapes. Students are instructed to look at the shape and decide which regular polygon best circumscribes the elements. By looking at the elements as regular polygons, students can better understand why the shapes have the symmetries that were identified in the previous lesson. After about three minutes, we go over their shapes and discuss the symmetries. This leads into the Mini-Lesson where students will identify the specific reflections and rotations that map a shape onto itself.

## Mini-Lesson

10 minutes

For the Mini-Lesson, I created a Geometer’s Sketchpad file, which students can use to investigate the rotational symmetry of quadrilaterals and regular polygons. Sometimes, I use the file as a presentation to the whole class and other times, I have the students use laptops to work with the file.  See my video ”Reflectional and Rotational Symmetry Quadrilatreals and Regular Polygons Mini Lesson” for an explanation on how the file can be used.

## Activity

23 minutes

In the activity, students look at nine different shapes and explore their reflectional and rotational symmetry.  Students work individually on all of the questions, but will discuss their answers with a partner throughout the activity.

In Part A of the worksheet, students identify shapes that have rotational symmetry after specific angles of rotation. These questions were designed to get students to think about how shapes with different orders of rotation can map onto themselves after rotations of the same measures. For example, a square has an order of rotation of 4 and a parallelogram has an order of 2, but they both map onto themselves after a rotation of 180o about their centers. After students work for about five minutes, they compare their answers with the students next to them to make sure they have identified all of the shapes for each question.

In Part B students choose four shapes and their partners choose four different shapes. After about 10 minutes, students share their answers with each other. They look at the their partner’s shapes and check to see if all of the lines of reflection and angles of rotation are identified for each shape. If one student leaves out or adds lines of reflection or angles of rotation, the other student can explain where his or her partner made an error and help to address the misconception (MP3).

## Summary

5 minutes
 Exit Ticket: Students will explain how they can find the angle of rotation that maps a polygon onto itself and explain what happens when a regular polygon is reflected in any of its lines of symmetry. This exit ticket assess how much the students understood from the lesson and allows me to make any necessary additions to future lessons.