Polygons With More Than 4 Sides
A. Parts of Polygons
Materials: Box of sticks, supplies “Polygons” drawer of the geometry cabinet
Presentation: Invite the child to choose any five sticks and write them. The teacher arranges the figures so that it is convex. Ask the child to count the sides and identify the figure – 5, pentagon. Give the nomenclature as before: surface, perimeter, side (sides),angle (angles), vertex (vertices). In order to make this figure stable the teacher attaches one stick and identifies it as a diagonal. Since it still is not stable, the teacher adds a second diagonal.
Notice that a triangle did not met a diagonal. The quadrilateral, having four sides (one more than the triangle) needed one diagonal to make it stable. This divided the quadrilateral into two constructive triangles. Here with a pentagon (having one more side than the quadrilateral) two diagonals were needed. They divided the figure into 3 constructive triangles. For a hexagon 3 diagonals will be needed.
Identify one angle. Next to it is a successive angle. The next angle is not successive, and there is a diagonal. The next angle is also not successive, and there is the other diagonal. The last angle is a succeeding angle. A line connecting this (first) angle with a succeeding angle is merely a side. However, a line connecting this angle with a non-successive angle forms a diagonal.
Examine the other angles as a focal point. Each time it is possible to make two diagonals, and three constructive triangles.
Take the polygon from its drawer. Ask the child to identify it and its particular characteristic – pentagon, having equal sides (turn it in its frame as proof) thus, a regular pentagon.
Repeat the nomenclature as before; everything is the same. There are three other parts which only pertain to the regular polygon. This knob indicates the center of the figure. A line form the center to any vertex is a radius. Even a line from the center to the midpoint of any side is also a radius, but it has a special name: apothem. Three period lesson.
Examine the other figures as well.