# Diagonals in Polygons (2-23 thru 3-1)

Finding patterns in the number of diagonals in polygons can be very challenging. First, the Mathletes had to draw all diagonals from a square to a regular 15-gon. Diagonals are segments that connect non-adjacent vertices. In other words, diagonals cannot lie on the side of a polygon. Many of the Mathletes saw patterns in the number of diagonals as the number of sides increased.

For the more advanced Mathletes, I was able to introduce a special algebraic formula for deternining the number of diagonals by taking half of the product of the number of sides and the number of sides minus three -- *n(n-3)/2 *with *n *being the number of sides of the polygon. So a 100-gon would have 100(97)/2 or 4,850 diagonals.

The Mathletes requested that I give them a 23-sided and 30-sided polygon so they could sketch more complex diagonals. See the attached pdf file.

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Diagonals_in_Polygons.pdf | 494.71 KB |