Przekątne wielokąta

Learning objectives

• You will develop the following competences: communicating in English, mathematical, IT and basic scientific and technical competence, your learning skills.

• You will get to know the concept and properties of the diagonals in the polygon.

• You will get to know the theorem about the diagonals.

Learning effect

• You will learn the concept and properties of the diagonals in the polygon.

• You will learn to apply the theorem about the diagonals.

Recollect the information about types and properties of polygons. The aim of the class is getting to know the concept and properties of the diagonal in a polygonpolygonpolygon. In a polygonpolygonpolygon, draw line segments, whose ends are the vertices of these polygons. Indicate the ones which are not the sides of the polygons. Find names of these line segments in the available sources.

• Think – does every polygonpolygonpolygon have the diagonals? What is the minimum number of vertices in a polygonpolygonpolygon to have the diagonals? Formulate the appropriate conclusion.

The conclusion: The polygonpolygonpolygon with the smallest number of vertices which has the diagonals is a quadrangle.

• Find out how many diagonals can be drawn from one vertex of a decagon, a 100‑gon, an n‑gon.

The conclusion: You can draw $(n-3)$ diagonals from one vertex of a polygon.

• Find the number of diagonals in any polygon. Formulate your conclusion.

The number of the diagonals in n–gon $(n\in N,n>3⩾)$ is expressed with formula $\frac{n(n-3)}{2}$.

Use the information to solve the tasks.

Having finished all the tasks, do the consolidation tasks. Formulate the conclusions that you need to remember.

• The diagonal of the polygondiagonal of the polygondiagonal of the polygon is the line segment joining two vertices and not being the side of the polygonpolygonpolygon.

• The polygonpolygonpolygon with the smallest number of vertices which has the diagonals is a quadrangle.

• The number of the diagonals in n –gon $(n\in N,n>3)$ is expressed with formula $\frac{n(n-3)}{2}$.

Exercises

Glossary

Keywords

diagonal of the polygondiagonal of the polygondiagonal of the polygon - the line segment joining two vertices and not being the side of the polygon,

number of the diagonals in the polygonnumber of the diagonals in the polygonnumber of the diagonals in the polygon,

penatgonpenatgonpenatgon,

polygonpolygonpolygon,

vertex of the polygonvertex of the polygonvertex of the polygon