The diagonals of a convex polygon are internal.
The convex polygon is one whose diagonals are always interior and its internal angles do not exceed pi radians or 180 degrees.
Before entering fully into the meaning of the concept, it is necessary to determine the etymological origin of the two words that give it shape: polygon derives from the Greek language, being the result of the sum of poly (which is synonymous with “many” ) and de gono (which can be translated as “angle” ); convex , for its part, emanates from Latin and is formed from the prefix con- (equivalent to “together” ) and the adjective vexus (which means “carried”).
Characteristics of a convex polygon
In the field of geometry , polygons are central elements that appear very frequently. This concept refers to plane figures composed of non-aligned straight segments, which are called sides .
The characteristics of polygons allow them to be classified in different ways. Regular polygons , for example, are those that have sides and interior angles that are congruent to each other. On the other hand, irregular polygons do not share this property.
In addition to everything stated above, it is worth knowing other unique data about convex polygons:
- All its vertices “point” to what is the outside of its perimeter.
- Triangles are all convex polygons.
- In the same way, we must not forget that regular polygons can also be said to be all convex.
Convex polygons have distinctive characteristics.
How to recognize it
There are several ways to find out if a polygon is convex. It must be taken into account that, in this type of figures, all of its vertices are pointed outwards; that is, outside. On the other hand, if a line is drawn on any side of the polygon, the entire figure will remain inside one of the semiplanes created by the line in question.
Another way to determine if a polygon is convex is by drawing segments between two points in the figure , regardless of their location. If these segments are always interior, it will be a convex polygon. If any segment is exterior, or if any of the internal angles exceed 180 degrees, the polygon will be concave.
It should be noted that a polygon can be convex and, in turn, be part of another of the aforementioned classifications (also being a regular polygon, to name one possibility).
The usual thing is that when talking about convex polygons, the term concave polygons also quickly appears. In this sense, it must be said that these are those that have one or more of their angles that are less than 180º. That is, so that it can be understood well, the latter are the ones who have some type of “incoming” in their figure.
How do you identify a concave one? Taking into account that the segment that joins two interior points of the polygon cannot be completely inside it.