Geometry – The Basics

Hello to all! Attentive readers of my blog know that I am a happy father of two children. The eldest – is already in full swing studying geometry and algebra, the younger – will approach the study of these subjects in a few years. Given that I studied geometry quite well at school, and I do not support most of the methods used in the modern education system – the current (as well as a few subsequent) entries will be devoted to the basics of geometry. I hope my son will like them, and you.

So what is geometry? (I still do not understand why the terms are crammed, but why not, the more so the definition of geometry is very simple). So, geometry is the branch of mathematics responsible for space. The name “Geometry” comes from the Greek words “Earth” and “Measuring” – i.e. We can say that Geometry is the science of measuring the earth.

The study of geometry is best started with a point – the simplest geometric figure.
geometry - point

In the text, dots are indicated in capital Latin letters or numbers. For example:
– completely equivalent terms denoting a point called A.

After the point, let’s move on to the line. The line has no beginning or end, which means that we can say that the line is infinite.

What follows from this? But only that:

  • Through two points you can draw a single line
  • geometry-line

  • Two lines can intersect at only one point (in the figure below, two lines intersect at point A)
  • геометрия - прямая - точка пересечения

  • Through one point you can draw an infinite number of lines (in the figure, several lines intersect at point A)
  • геометрия - точка пересечения прямых
    Lines are also denoted by Latin letters, but lowercase. Those. line “a” is the designation of the line 🙂
    At the same time, if we want to designate a line on which two points are located, then we need to write: line AB.

    After the straight line, let’s move on to the beam. What is a ray? It is a line located on one side of a point. So – the ray has a beginning, but no end (in the figure below – the ray f, with the beginning at point A and point B located on this beam).
    геометрия - луч

    Rays are indicated by lowercase Latin letters: ray “a”, or – two lowercase letters, if we are talking about the first point, which is the beginning of the ray, and the second point, which is located on this ray: ray AB.

    The question arises – what will happen if we take a ray (coming from point a) and limit it to a certain length? There is a segment. A line is a part of a line that is limited by the beginning and end.
    The segment is indicated in capital Latin letters (the figure below shows the segment AB):
    геометрия - отрезок

    Many segments connected in one or another sequence form a broken line. In general, the definition of a broken one is more correct: a broken line is a geometric figure consisting of points that are connected by segments, but the essence doesn’t seem to change from this, right? The vertices of the broken are the points at which the segments of which the broken consists are connected, and the segments of the broken form its links. It is indicated broken in capital Latin letters:
    The broken line is “ABCD”, where the vertices of the broken line are A, B, C, D, and the links of the broken line are AB, BC, CD.
    геометрия - ломаная

    Given that the polyline consists of segments of a certain length – to find the total length of the polyline, you need to add all the links of the polyline (an example – in the figure below):
    геометрия - ломаная - общая длина

    It’s enough for today. We examined the basics of geometry, and very soon we will proceed to consider such a concept as “Angle”.

    Thanks for your attention!