In this problem, we want to determine if a convex polygon has at least one diagonal outside the polygon.
There are two types of polygons we see in geometry:
A convex polygon, which contains angles that are strictly less than 180 degrees. For example, a regular hexagon:
The second is a concave polygon, which can include angles that are greater than 180 degrees. Here's a concave hexagon:
The marked angle shows a reflex angle that is larger than 180 degrees.
To determine if a convex polygon can have an external diagonal, we can look at an extreme case:
This hexagon is considered convex because all the angles are less than 180. If we try to draw diagonals, we get:
Even for the largest angles, the diagonals are never outside the interior of the shape.
Therefore, the answer is false.