6.. Plane figures
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, иии, the sides by a, b, c, d, иии, the angles by a , b , g , d , иии, and the polygon itself by ABCD иии. 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, иии.
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 й й 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.