Mathematics Related to the Pentagon Sketch
From the pentagon sketch, you can see that five side lengths do not uniquely determine shape. When you drag corner points on the pentagon, the angle measures, shape, and area change but the side lengths do not. Using the pentagon sketch, you can investigate questions such as: For a pentagon that has all sides congruent, what is the minimum number of angles that need to be fixed at a specific measure in order to ensure that the pentagon is regular?
In general, side lengths do not uniquely determine the shape of polygons. However, as you may know, side lengths do uniquely determine the shape of triangles. Triangles can be uniquely determined in several ways - for example, three sides (SSS), two sides and the included angle (SAS), or two angles and the included side (ASA).