What is called a straight ray segment. How is the beam indicated in the notebook? side BC and side CD are adjacent
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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 a triangle, square, rectangle, parallelepiped, circle, oval, rhombus, cylinder, etc. The simplest figure 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.
This is interesting: how area is designated, examples for calculation.
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).
A geometric figure with angles is based on half-lines. 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 that define a straight line on a plane.
Notation in geometry
There are several designation options:
Need to know: What is horizontal 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.
A point and a straight line are the basic geometric figures on a plane.
The ancient Greek scientist Euclid said: “a point” is something that has no parts.” The word “point” translated from Latin means the result of an instant touch, an injection. A point is the basis for constructing any geometric figure.
A straight line or simply a straight line is a line along which the distance between two points is the shortest. A straight line is infinite, and it is impossible to depict the entire straight line and measure it.
Points are denoted by capital Latin letters A, B, C, D, E, etc., and straight lines by the same letters, but lowercase a, b, c, d, e, etc. A straight line can also be denoted by two letters corresponding to points lying on her. For example, straight line a can be designated AB.
We can say that points AB lie on line a or belong to line a. And we can say that straight line a passes through points A and B.
The simplest geometric figures on a plane are a segment, a ray, a broken line.
A segment is a part of a line that consists of all points of this line, limited by two selected points. These points are the ends of the segment. A segment is indicated by indicating its ends.
A ray or half-line is a part of a line that consists of all points of this line lying on one side of a given point. This point is called the starting point of the half-line or the beginning of the ray. The beam has a starting point, but no end.
Half-lines or rays are designated by two lowercase Latin letters: the initial and any other letter corresponding to a point belonging to the half-line. In this case, the starting point is placed in the first place.
It turns out that the straight line is infinite: it has neither beginning nor end; a ray has only a beginning, but no end, but a segment has a beginning and an end. Therefore, we can only measure a segment.
Several segments that are sequentially connected to each other so that the segments (neighboring) that have one common point are not located on the same straight line represent a broken line.
A broken line can be closed or open. If the end of the last segment coincides with the beginning of the first, we have a closed broken line; if not, it is an open line.
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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.
Goals:
- Introduce students to the concept of a ray as an infinite figure;
- Learn to show the beam using a pointer;
- Continue building computing skills;
- Improve problem solving skills;
- Develop the ability to analyze and generalize.
During the classes
I. Organizing time.
Guys, are you ready for the lesson? ( Yes. )
I count on you, friends!
You are a good friendly class.
Everything will work out for you!
II. Motivation for learning activities.
I really want the lesson to be interesting, informative, so that together we repeat and consolidate what we already know and try to discover something new.
III.Updating knowledge.
- Read the numbers and name the “extra” number in each row:
a) 90, 30, 40, 51.60;
b) 88, 64,55,11, 77, 33;
c) 47, 27, 87, 74, 97, 17; - List the numbers in order:
a) from 20 to 30;
b) from 46 to 57;
c) from 75 to 84; - Do you think these texts will be tasks?
Change the question in the second text so that it becomes a task.
Change the condition so that the text becomes a task.
Solve the given problems.
IV. Primary assimilation of new knowledge.
Draw a line like this.
What is it called?
Draw a line like this.
What is it called? What is the difference between a segment and a straight line?
Draw a line like this.
Who knows what it's called?
Look at the picture, you see similar lines, what is it?
This line is called a ray. How does it differ from a straight line and a segment?
This is a very interesting figure: it has a beginning and no end.
And this is how they portray her. ( Work on the board and in notebooks.) Mark a point, apply a ruler to it and draw a line along the ruler.
No matter how long the ruler is, we still won’t be able to draw the entire beam. In the figure we have depicted only part of the beam, which shows the direction of the beam.
The beam can be drawn in any direction:
Draw three different rays in your notebook.
To distinguish one ray from another, we will agree to denote the ray with two letters of the Latin alphabet in the same way as we denoted segments. The letters must be written in a strictly defined order: the first letter is written that indicates the beginning of the beam, the second is written above or below the beam.
Look at the picture in the textbook. The red beam is indicated by two letters. What letter indicates the beginning of the ray?
Let's read the entry together: “Beam AB”
Now read the following entries: beam BC, beam MK, beam BA, beam OX.
It is important to learn how to show the beam correctly. We will do this with the end of the pointer. ( Demonstration by the teacher.)
Now look at the poster. ( Prepared in advance, it has 3 rays.) It shows 3 rays. Read the title of each one. When naming a beam, show it with a pointer.
Fizminutka
1, 2, 3, 4, 5
We all know how to count.
We also know how to relax:
Let's put our hands behind our backs,
Let's raise our heads higher
And let's breathe easily.
One, two - head up,
Three, four - the legs are wider,
Five, six - quiet network.
Once - get up, stretch.
Two – bend over, straighten up.
Three - three claps of your hands,
Three nods of the head.
By four – your arms are wider.
Five - wave your arms.
Six - sit quietly at your desk.
V.Initial check of understanding.
1) Working with the textbook.
Is it possible to draw the entire beam?
In what direction can the ray be drawn?
Students name each ray by first reading the letter corresponding to the beginning of the ray.
Students draw a ray in their notebooks and label it with letters.
Place point O in your notebook. Draw a straight line through it. How many rays did you get?
Draw another straight line through this point. How many rays are there now?
VI. Organization of mastering methods of activity.
1) Work in a printed notebook.
Differentiated task.
1st group - No. 19
2nd group - No. 20
3rd group - No. 21
2) Fizminutka - ophthalmic simulator.
3) Working from the textbook
Read what addition methods did Znayka come up with?
Find the results of addition using the same methods.
What is known about the problem?
What do you need to know?
In short – is it more or less?
How to find out the length of a pencil?
Write down your answer.
VII. Reflection.
What new did you learn in the lesson?
What is a beam?
How to draw a ray?
How many rays can be drawn through one point?
Today in class they helped me.....
VIII. Homework.
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? A mathematical point has no dimensions and is designated by capital 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