Diagonals in a Polygon

By

Danielle Habeeb

A diagonal is a line segment that connects non-adjacent vertices in a polygon. Consider the number of diagonals in a triangle, quadrilateral, pentagon, hexagon, heptagon, and octagon. What pattern do you notice? Use this pattern to predict the number of diagonals in a dodecagon.

First, create three segments to form a triangle. Since you are looking for diagonals you should connect a segment vertex to vertex but the segments cannot be adjacent. Therefore, the triangle has no diagonal line segments.

Next, create a quadrilateral. Connect each vertex with a line segment. You should see that there are only two possible diagonal segments.

Then, construct a pentagon. Again, connect all vertices until all possible diagonal segments are constructed. You should find that a pentagonal figure should have 5 diagonal segments.

Create a hexagonal figure. Connect all vertices until all possible diagonals have been created. When finished you should have 8 diagonal segments.

Create a heptagon. Connect all vertices until all possible diagonals have been connected. You should have connected 12 different diagonals.