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 beam has one extreme point, in which it begins. It's called 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 at 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.
The rays coincide if they lie on the same straight line and have general beginning 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.
We all once studied geometry at school, but not all of us remember what a segment is. And even more so, few people can explain the concept of rays and how they are designated. Let's try in this article to remind ourselves of these definitions and consider them in mathematics. We will also define what a beam is and how it differs from light. If you get into it, it won't be difficult to understand.
Definition of concepts
First, let's remember what is called geometry. Geometry is a branch of mathematics that studies geometric figures and their properties. These include triangle, square, rectangle, parallelepiped, circle, oval, rhombus, cylinder, etc. The simplest figure- this is a straight line. It is endless and has no beginning. Two lines will intersect only at one single point. Countless straight lines can be drawn through one point. Every point on a line divides it into two.
It consists of points located on one side. All concepts of these subsets can be named this way. The ray is denoted by one lowercase Latin letter or two capital letters, when one point is the beginning (for example, O), and the second lies on it (for example, F, K and E).
At the core geometric figure having angles lie half-line. They start at the point where they intersect, but the other side is directed to infinity. The beginning divides the line into 2 parts. In writing it is usually referred to as two capitals (OF) or one Latin letter (a, b, c). If a straight line is given, then OB is written in rounded brackets: (OB). If this is a segment - in square brackets.
Thus, a ray is part of a straight line. Through any point you can draw many straight lines, but through 2 non-coinciding ones - only one. The latter can interact only in three ways: intersect, cross, or be parallel to each other. There are linear equations, which define a straight line on the plane.
Notation in geometry
There are several designation options:
Need to know: What is and horizontal position?
The difference between light rays and geometric ones
In geometry, these concepts are very similar. A ray is a line, but it is the energy of light. In other words, it is a small beam of light. In optics this concept, like the concept of a straight line, is basic in geometry. The light does not have a concentrated direction, diffraction occurs. But when the light flux is very strong, divergence is neglected and a clear direction can be identified.
We will look at each of the topics, and at the end there will be tests on the topics.
Point in mathematics
What is a point in mathematics? Mathematical point has no dimensions and is indicated in capitals in Latin letters: A, B, C, D, F, etc.
In the figure you can see an image of points A, B, C, D, F, E, M, T, S.
Segment in mathematics
What is a segment in mathematics? In mathematics lessons you can hear the following explanation: a mathematical segment has a length and ends. A segment in mathematics is the set of all points lying on a straight line between the ends of the segment. The ends of the segment are two boundary points.
In the figure we see the following: segments ,,,, and , as well as two points B and S.
Direct in mathematics
What is a straight line in mathematics? The definition of a straight line in mathematics is that a straight line has no ends and can continue in both directions indefinitely. A line in mathematics is denoted by any two points on a line. To explain the concept of a straight line to a student, you can say that a straight line is a segment that does not have two ends.
The figure shows two straight lines: CD and EF.
Beam in mathematics
What is a ray? Definition of a ray in mathematics: a ray is a part of a line that has a beginning and no end. The name of the beam contains two letters, for example, DC. Moreover, the first letter always indicates the starting point of the beam, so letters cannot be swapped.
The figure shows the rays: DC, KC, EF, MT, MS. Beams KC and KD are one beam, because they have a common origin.
Number line in mathematics
Definition of a number line in mathematics: a line whose points mark numbers is called a number line.
The figure shows the number line, as well as the ray OD and ED
Beam and straight line are among the main 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 one side emanating from specific point, on the other hand, it is not limited by anything.
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 it straight arbitrary point, then departing from it endless line 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 two is used in capital letters: NK beam 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, use lowercase letter the straight line on which the beam is located is indicated. 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.
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Books
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