Convex and Non-convex Polygons
Convex and non-convex polygons are classifications of polygons. But what are polygons? Polygons are closed-plane figures made up of line segments and the segments intersect only at their endpoints. If it does not satisfy the definition, then it is considered not a polygon. A three-dimensional figure is not a polygon since it is not anymore a plane figure. A plane figure has only two dimensions, namely, length and width. Also, a polygon’s sides must have exactly two other sides connected to them at their endpoints. All the sides must be line segments, not curve or circular in manner. Therefore, figures like circles, cones and the like are not polygons.
So how do we classify them?
Here are some of the conditions in order for a polygon to be called convex polygons:
- When the sides of the polygons are extended, no extended line contains a point in the interior of the polygon.
- If no diagonal is in the exterior of the polygon.
- If no interior angle of the polygon is greater than 180˚.
On the other hand, polygons are called non-convex if:
- A line passes through the interior of the polygon when the sides are being extended.
- One of its diagonals is found in the exterior of the polygon.
- One of its angles measures more than or greater than 180˚.
What does a diagonal mean? A diagonal is a segment connecting two non-consecutive vertices of a polygon. The number of diagonals in a polygon will depend on the number of sides a polygon has. The greater the number of sides, the larger the number of its diagonals. It is important to determine the number of diagonals a polygon has since it plays an important role in determining the sum of the interior angles of a polygon.
