Lesson 11

Lesson 11 Summary

 

Polygons can be found in building structures, floor tiles, pavement, art motifs, quilts, games, and puzzles. Designers, artists, puzzle makers, and architects have for centuries used their understanding of the angles of polygons to create successful designs. Their knowledge of the measures of angles in a polygon is applied to ensure that the shapes are arranged correctly. This helps them choose the correct shapes and visualize the final design.

 

An understanding of the angles of polygons is an important part of ensuring that the design works. For example, a master tiler can use his or her understanding of the angles in polygons to choose tiles and then arrange them to produce visually stimulating, complex patterns. A puzzle maker can use seven different polygons to create many different tangrams. In this lesson you used your understanding of the properties of angles and polygons to solve a variety of layout and design problems.

 

You used your knowledge of the sum of the measures of the angles in a triangle to determine a formula for the sum of the measures of the angles in any convex polygon. The sum of the measures of the interior angles in a polygon was used to determine the measure of an interior angle in any regular polygon. You then applied your knowledge of exterior angles to prove that the sum of the measures of the exterior angle of any convex polygon is 360°.

 

In the module project you applied the concepts you learned in this module to design and then analyze a pattern or game.

 

You have used reasoning to solve a wide variety of problems. Refer to the Module 2 Summary for an overview of concepts you investigated in this module.