If a point travels in a plane, its path
generates a **plane
figure**. If it moves consecutively
along segments linking several points, it generates a **line figure**, if it travels along curves linking
points, a **curved
figure**.** **

If a
point returns to its starting point, the curve becomes **closed**. A closed line figure is a **polygon**. The most familiar closed **curved figure**** **is the **circle**. Because a closed line isolates a part
of the plane, it is called its **boundary**, its interior the **area** of the figure.

If the point does not return to
its starting position, you obtain an **open** **figure**. A path that contains several straight
sections is **polygonal****.** A** **curved** **figure
is generated, when you throw a ball at an acute angle to the
ground or spray the lawn with a thin jet of water.

Sometimes **points**** **and **segments** are inluded among **plane
figures**, because
they are their simplest representatives.

The segments of the boundary of
a **polygon** are called **sides****, **their end points** ****corners ****or**** ****vertices**. Sections of a polygonal border, which
are formed by two adjacent sides and their inward extensions, are
called **angles****.**** ****Angles and sides form polygons.** You denote the corners by *A, B, C,
D, *···, the sides by *a, b, c, d, *···, the
angles by *a** , **b** , **g** , **d* , ···, and the polygon itself by *ABCD ···. *Lines
between vertices, which are not adjacent, are called diagonals.

Polygons are classified
according to the number of their corners, whence one talks of **Triangles**, **Tetragons**, **Pentagons**, ···.

**The
triangle is the simplest polygon**.
Its **sides** *a, b, c *lie **opposite** to *A,
B, C, *and its **angles** *a** , **b** , **g* are at the **vertices*** A, B, C*.

The angles at the vertices are **adjoin** the respective sides. An angle which is formed by two
sides of a triangle is **enclosed
by the sides**.

A** ****triangle **with two equal sides is **isosceles**, one with all equal sides an **equilateral**.

**Quadrangles** can
have very different shapes. Besides ordinary ones you meet those
with **reentrant
**angles and
even overlapping ones. If in an ordinary quadrangle *ABCD *the
sides *AB = AD *and *CB = CD, *its is called a **rhombus***. *If a quadrangle's sides are
perpendicular to each other at each corner, it is called a **rectangle****, **if moreover they are
equal, it is called a **square**.

The
straight sides which lie opposite to each other in a rectangle,
are said to be **parallel** and the symbol ½ ½
is used for this property.

If in a
quadrangle only one pair of opposite sides are parallel, it is
called a** ****trapezoid****, **if two non-parallel
sides are equally long, it is said to be **isosceles****. **If both pairs of
opposite sides are parallel, a quadrangle is called a **parallelogram**, if all sides are equal, a **rhombus**.

The variety of polygons increases with the number of vertices. This is shown by some of the figures at the beginning of this section.