The ownership of the terminology, as well as the knowledge of the properties of various geometric shapes will help in solving many geometry tasks. Studying such a section as a planimetry, the student is not rarely encountered by the term "polygon". What figure does this concept characterizes?
Polygon - definition of a geometric shape
The closed broken line, all sections of which lie in the same plane and do not have sections of self-intersection, forms a geometric shape called a polygon. The number of loloral links should be at least 3. In other words, a polygon is defined as part of the plane, the boundary of which is a closed broken broken.
In the course of solving problems with the participation of a polygon, often appear such concepts as:
- Polygon side. This term characterizes the segment (link) of the broken chain the desired figure.
- The angle of the polygon (internal) is an angle that form 2 adjacent lolorals.
- The top of the polygon is defined as the peak of the broken.
- The diagonal of the polygon is a segment connecting any 2 vertices (except the adjacent) polygonal figure.
At the same time, the number of links and the number of vertices of broken within one polygon coincide. Depending on the number of angles (or broken sections, respectively), the type of polygon is determined:
- 3 corners - triangle.
- 4 corners - quadrangle.
- 5 angles - pentagon, etc.
If a polygonal figure has equal angles and, accordingly, the parties, they say that this polygon is correct.
Types of polygons
All polygonal geometric shapes are divided into 2 types - convex and concave.
- If any of the sides of the polygon after continuing to direct does not forms with the actual figure of the intersection points, you have a convex polygonal figure.
- If after continuing the side (any) the resulting direct crosses the polygon, we are talking about a concave polygon.
Properties of a polygon
Regardless of whether the studied polygonal figure is correct or not, it has the properties below. So:
- Its internal angles are summarized (p - 2) * π, where
π is the radical measure of the expanded angle, corresponds to 180 °,
p is the number of angles (vertices) polygonal figure (p-square).
- The number of diagonals of any polygonal figure is determined from the P * (P - 3) / 2 ratio, where
p is the number of sides of the p-square.
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