What is called a straight ray segment. side EF and side FA are adjacent

Along with such concepts as point, segment, line, there is one more concept in geometry. It is called ray. A ray is a part of a straight line, limited on one side by a point, and on the other side - infinite, i.e. not limited by anything.

An analogy can be drawn with nature. For example, a beam of light that we can direct from earth into space. On the one hand it is limited, but on the other hand it is not. Each ray has one extreme point at which it begins. It's called the beginning of the ray.

If we take an arbitrary straight line a, and mark some point on it ABOUT, then this point will split our line into two parts. Each of which will be a ray. Point O will belong to each of these rays. Point O will be in this case the beginning of these two rays.

The beam is usually designated by one Latin letter. The figure below shows ray k.

You can also denote the beam with two capital Latin letters. In this case, the first of them is the point at which the beginning of the beam lies. The second is the point that belongs to the ray, or in other words, through which the ray passes.

The figure shows the OS beam.

Another way to designate a ray is to indicate the starting point of the ray and the line to which this ray belongs. For example, the figure below shows the ray Ok.

Sometimes they say that the ray comes from point O. This means that point O is the beginning of the ray. Rays are also sometimes called semi-straight.

Task:

Draw a straight line and mark points A B on it and mark point C on segment AB. Among the rays AB, BC, CA, AC and BA, find pairs of coinciding rays.

Solution:

The rays coincide if they lie on the same straight line and have a common origin and none of them is a continuation of another ray.
The figure shows that these conditions are met by rays AB and AC, as well as rays BC and BA. Therefore, they are coincident.

Answer: AB and AC, BC and BA.

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Most often this question is asked in schools, in geometry lessons, and the concept is also quite popular in optics. However, as often happens, the word has quite a few meanings. It’s worth taking a closer look at the most key ones.

Geometry

In order to understand what a ray is from the point of view of geometry, you need to consider one of the fundamental concepts of this science, namely the straight line.

It is quite difficult to define this term, since it is one of the original ones, and it is with the help of a straight line that other various words are explained. There are quite a few axioms on this matter. However, a straight line can be interpreted as a line between two points.

A straight line has its own properties, according to Euclidean geometry.

Through any point you can draw as many straight lines as you like, but through two divergent points you can only draw one.
Lines can be in only three states - they can intersect, be parallel to each other, and can also cross.
There is a linear equation that defines a line on a plane.

So, it's worth returning to the concept of a ray. It is part of a straight line. If you put a point on such a line, you will automatically get two rays, and they will not have a second point limiting them.

Thus, ray is part of a straight line having a beginning but no end.

Light beam

Geometric optics treats the concept of a light ray in a fairly similar way. Here it will also be a line, but it will be used by light energy. In other words, a light beam is small beam of light.

Just like the concept of a straight line in geometry, the concept of a ray in optics is a fairly basic phenomenon. However, unlike a geometric beam, a light beam does not have any clear direction, since diffraction occurs. However, if the light is very large, then the divergence is usually neglected. In this case, a clear direction can be identified.

In addition to basic terms in the exact sciences, this word refers to a wide variety of objects. For example, about seven sports clubs had this name, and some of them still exist. Many villages, towns and hamlets in Russia, Ukraine and Belarus are also called Luchi. Ships are not far behind them - and in this case, Luch is a brand of passenger ships, as well as a whole class of yachts.

These yachts are single-seaters and are used for racing. They are often used as educational equipment for children, but competitions are also held on them.

There are other meanings:

This word refers to three Russian relay satellites.
A magazine with the same name is published in Udmurtia and the Urals.
The unification of the nuclear industry was also called the Beam.
There is a watch factory and a shoe factory in Minsk with this name.
Luch is the pseudonym of a Chuvash writer, whose official name is Grigory Vasilyevich Vasiliev.

The ray and the straight line are among the basic geometric elements. Information about them is given already at the first stage of studying the corresponding section of mathematics. What is the difference between a ray and a straight line? Information about this is provided below.

Definition

Beam- this is a half-line, on the one hand emanating from a specific point, on the other - unlimited.

Straight- this is a line that is infinite on both sides, passing through any two points and does not change its direction (unlike a curve or broken line).

Straight

Comparison

From the definitions it is clear that the cardinal difference between a ray and a straight line lies in whether they are limited in space. Thus, the beam necessarily has a beginning and continues only on one side. A straight line, in turn, has no limit on either side. In this regard, only part of it can be drawn, which, incidentally, also applies to the ray.

If you take an arbitrary point on a straight line, then the infinite line extending from it will be a ray. In this sense, the ray can be called part of a straight line. It is also true that the chosen point will serve as a starting point for two oppositely directed rays at once.

Comparing a ray and a straight line, it should be said about the ways of designating them. Each of the geometric objects can be called by a Latin small letter: ray a (c, d, t) or straight line b (a, h, c). Also, in both cases, the designation is used in two capital letters: ray NK or straight OD.

However, there are differences in the last point. The letters in the name of a line, marking the points through which it is drawn, can be swapped when reading and writing. Meanwhile, relative to the ray, the first point is strictly its beginning, and then the point located at a certain distance from the original one.

In addition, the beam has its own version of the designation. In this case, after the capital character naming the starting point, the straight line on which the beam is located is indicated using a lowercase letter. Thus, the notation Bo is interpreted as follows: a ray with origin at point B belongs to the straight line o.

What is the difference between a ray and a straight line, besides what has been said? The fact is that the rays can form an angle. To do this, they must originate from one point. Right angles do not form.

the beginning of the ray.

a ABOUT

ray k.

semi-straight.

Task:

The figure shows that these conditions are met by rays AB and AC, as well as rays BC and BA. Therefore, they are coincident.

Answer: AB and AC, BC and BA.

The beam is usually designated by one Latin letter. The figure below shows ray k.

The figure shows the OS beam.

Another way to designate a ray is to indicate the starting point of the ray and the line to which this ray belongs. For example, the figure below shows the ray Ok.

Sometimes they say that the ray comes from point O. This means that point O is the beginning of the ray. Rays are also sometimes called semi-straight.

Task:

Draw a straight line and mark points A B on it and mark point C on segment AB. Among the rays AB, BC, CA, AC and BA, find pairs of coinciding rays.

From the school geometry course, few people have accurate information about what a segment is, how it is designated, what a broken line, a straight line, a point are, and how rays are designated. If you cannot remember the initial geometry course, just read this article.

What is geometry? This is a mathematical section in which the student gets acquainted with geometric figures and their properties. There is a lot of information, sometimes there is not enough time to take in and remember everything. Some knowledge needs to be refreshed after several months and even years. For example, remember what rays are and how they are designated.

What is a ray in geometry

A ray is a straight line, limited on one side by a point, and on the other hand free, that is, without restrictions. To quickly remember how rays are designated and what they look like, you can give a simple example: we can direct a beam of light from a flashlight into the sky, right? On one side, the beam is limited - from the place where it comes out, that is, from the flashlight. On the other hand, it has no restrictions. It turns out that there is only one extreme point of the beginning of the ray, and it is called the “beginning”. The second point does not exist, because the beam goes to infinity.

To understand how to mark a ray on a piece of paper, you need to draw a straight line. For example, let it be a segment equal to 10 cm. On the right side we will put a limit - a dot, this is the beginning of the ray. There will be no second point at the end of the segment.

How are the rays designated?

Let's continue to remember what a ray is and how to designate it.

There are several designation options:

Let's draw a straight line in a notebook and mark the point of origin of the ray. And let's give it a name. For example, let it be beam "C". The first point is the beginning of the ray; the second point, as you already remembered, does not exist. This is the classic ray notation scheme.
The second option is more interesting: the beam can be designated by several letters. For example, there can be 2 letters on one beam. The first is the beginning of the beam, let it be the letter A, and the second can be located with a certain step. Let’s say that on a segment 10 cm long, the beginning of the ray is designated by the letter A, and at a distance of 4 cm from the beginning of the ray there is a second point, point B. Then the ray should be designated as ray “AB”. To make it clearer, you can read it like this: the second point B is the point through which the beam passes.
The rays can also be designated in a third way, when the starting point is not at the beginning of the ray, but with a slight deviation. For example, draw a straight line 10 cm long, step back 1 cm from the left edge, put a dot - this will be the beginning of the ray. We denote, for example, the letter O. We do not put a point in the middle of the ray, but we denote this part of the ray with the letter K. In this case, the letter O will be the beginning of this ray, it comes from this point. The beam is read like this: “OK”, it is semi-direct.

How is a beam indicated in a notebook?

The designation on the letter of the ray must be remembered once: the rays are written in Latin capital letters. If it is a straight line, then you need to write the ray AB in parentheses: (AB). If you have a segment in front of you, then it is written only in square brackets.

Geometry

In order to understand what a ray is from the point of view of geometry, you need to consider one of the fundamental concepts of this science, namely the straight line.

A straight line has its own properties, according to Euclidean geometry.

Through any point you can draw as many straight lines as you like, but through two divergent points you can only draw one.
Lines can be in only three states - they can intersect, be parallel to each other, and can also cross.
There is a linear equation that defines a line on a plane.

Thus, ray is part of a straight line having a beginning but no end.

Light beam

Geometric optics treats the concept of a light ray in a fairly similar way. Here it will also be a line, but it will be used by light energy. In other words, a light beam is small beam of light.

In addition to basic terms in the exact sciences, this word refers to a wide variety of objects. For example, about seven sports clubs had this name, and some of them still exist. Many villages, towns and hamlets in Russia, Ukraine and Belarus are also called Luchi. Ships are not far behind them - and in this case, Luch is a brand of passenger ships, as well as a whole class of yachts.

These yachts are single-seaters and are used for racing. They are often used as educational equipment for children, but competitions are also held on them.

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