Intent In this activity, students reflect on and apply their knowledge of the relationship of sides and angles in polygons. This activity emphasizes the important mathematical relationships they have worked on recently, including the unproven fact that the sum of the angles in a triangle is 180° and, based on this conjecture, the proven polygon angle sum formula.

Mathematics This activity draws upon the polygon angle sum formula to introduce the concept of a regular polygon, a polygon in which all angles have the same measure and all sides are the same length. Students draw and measure angles using a protractor one more time.

Progression This activity serves as a wrap-up for the angle and polygon investigation sequence. After recalling and writing about what they know about polygon angles, students solve the angle measures of a regular pentagon and regular octagon and then draw these polygons.

Approximate Time 20 minutes for activity (at home or in class) 10 minutes for discussion

Classroom Organization Individuals, followed by small groups

Materials Protractors

Doing the Activity This activity requires little or no introduction.

Discussing and Debriefing the Activity You may want to have one or two volunteers read or present their work on Question 1 and then allow the class to add to or to correct the material presented. Be sure to get some explanations for the angle sum formula. These might refer, for example, to the idea of dividing a polygon into triangles or to the numerical pattern found in Polygon Angles. For Question 2, ask students to explain their work. Use the opportunity to briefly emphasize the definition and basic properties of a regular polygon. Then ask what difficulties students had in drawing the polygons. In Question 3, students are asked once more to use protractors to draw polygons, reinforcing their grasp of the pattern developed in the previous activities. If they correctly determine the size of each angle in a regular polygon, and measure correctly, their figures should close—that is, the last side of each figure should meet the first side at the final vertex.