CHAPTER II

On Triangles

21. A plane region bounded by line segments is called a polygon (Fig 18).

The segments are called the sides of the polygon, and their endpoints are called its

vertices.

In fact, we will generally use the term polygon only for a portion of the plane

bounded by a single contour which can be drawn with a single continuous stroke.

The plane region which is shaded in Figure 19 will not be a polygon for us.

Figure 18

Figure 18b Figure 19

A polygon is said to be convex (Fig. 18) if, when we extend any side indeﬁnitely,

none of the lines thus formed crosses the polygon. In the opposite case (Fig. 18b)

the polygon is said to be concave.

Polygons are classiﬁed according to the number of sides they have. Thus the

simplest polygons are: the polygon with three sides or triangle, the polygon with

4 sides or quadrilateral, the polygon with 5 sides, or pentagon, the polygon with

six sides or hexagon. We will also consider polygons with 8, 10, 12, and 15 sides,

called octagons, decagons, dodecagons, and pentadecagons.

Any segment joining two non-consecutive vertices of a polygon is called a di-

agonal.

Remark. More generally, an arbitrary broken line, even one whose sides cross

(as in Fig. 19b), will sometimes be called a polygon. In this case, when the broken

line does not bound a unique region, the polygon is said to be improper. However,

when we want to specify that the polygon is of the ﬁrst type (Figures 18 and 18b),

and not like the one in Figure 19b, we will speak of a proper polygon.

22. Among triangles we distinguish in particular:

The isosceles triangle. This name is used for a triangle with two equal sides.

The common vertex of the equal sides is called the vertex of the isosceles triangle,

and the side opposite the vertex is called the base;

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