Draw polygons from a triangle to an octagon on the board. Ask student volunteers to come to the board and identify each type of polygon and then fill in diagonals, after you've explained the concept of the diagonal. This will be simple for your students once they understand the idea, which is important when you are introducing new terminology.
Once your students understand the concept of the diagonal, lead a discussion about the number of diagonals and the number of sides for each one, making a chart with two columns: sides and diagonals. Triangles have three sides but no diagonals (3, 0). Quadrilaterals have four sides and two diagnoals. Pentagons have five sides and five diagonals. See if your class can figure out the formula, which is (n(n-3))/2 for an n-sided polygon.
You'll need a large protractor for this activity. Draw polygons from three to eight sides on the board and then ask students to come up and measure the angles at each vertex. If you draw regular polygons, they'll only need to do this once per polygon. This will show students how to use protractors and will also give you a chance to introduce them to another polygon-related formula in the next section.
For any polygon with n sides, the sum of the interior angles is (n-2)180. So a triangle, which has three sides, has three angles which will add up to 180 degrees. A square or rectangle (or other quadrilateral) has four angles which will make 360 degrees. Make a chart with sides and sum of angles as your column headings and see if students can figure out the formula with your guidance.