## Task 3 - 050513

Construct a regular hexagon! Draw all possible diagonals into the hexagon! How many diagonals do you find? List them by naming them (e.g., $A B, \ldots$ )!
From each vertex of the hexagon, five segments extend to the other vertices. Since each segment has a starting and an endpoint and is thus counted twice in this consideration, there are $\frac{6 \cdot 5}{2}=15$ segments in the hexagon.

Since the six sides of the hexagon do not count as diagonals, there are still 9 left, i.e., there are nine different diagonals in a hexagon, as shown in the figure:

$$
A C, A D, A E, B D, B E, B F, C E, C F, D F
$$