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§one. test questions
Question 1. Give examples of geometric shapes.
Answer. Examples of geometric shapes: triangle, square, circle.

Question 2. Name the basic geometric shapes on the plane.
Answer. The main geometric figures on the plane are the point and the line.

Question 3. How are points and lines defined?
Answer. Points are indicated by capital Latin letters: A, B, C, D, .... Straight lines are denoted by lowercase Latin letters: a, b, c, d, ....
A line can be denoted by two points lying on it. For example, line a in figure 4 could be labeled AC, and line b could be labeled BC.

Question 4. Formulate the basic properties of membership of points and lines.
Answer. Whatever the line, there are points that belong to this line, and points that do not belong to it.
Through any two points you can draw a line, and only one.
Question 5. Explain what a segment with ends at given points is.
Answer. A segment is a part of a straight line that consists of all points of this straight line that lie between two given points of it. These points are called the ends of the segment. A segment is indicated by indicating its ends. When they say or write: "segment AB", they mean a segment with ends at points A and B.

Question 6. Formulate the main property of the location of points on a straight line.
Answer. Of the three points on a line, one and only one lies between the other two.
Question 7. Formulate the main properties of measuring segments.
Answer. Each segment has a certain length greater than zero. The length of a segment is equal to the sum of the lengths of the parts into which it is divided by any of its points.
Question 8. What is the distance between two given points?
Answer. The length of segment AB is called the distance between points A and B.
Question 9. What are the properties of splitting a plane into two half-planes?
Answer. The partition of a plane into two half-planes has the following property. If the ends of any segment belong to the same half-plane, then the segment does not intersect the line. If the endpoints of a segment belong to different half-planes, then the segment intersects the line.

Point and line are the main geometric figures on the plane.

The ancient Greek scientist Euclid said: “a point” is that which has no parts.” The word "point" in Latin means the result of an instant touch, a prick. The point is the basis for constructing any geometric figure.

A straight line or just 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 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, the line a can be denoted by AB.

We can say that the points AB lie on the line a or belong to the line a. And we can say that the line a passes through the 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, which consists of all points of this line, bounded 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, which consists of all points of this line, lying on one side of its given point. This point is called the starting point of the half-line or the beginning of the ray. A ray has a start point but no end point.

Half-lines or rays are denoted 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 line is infinite: it has neither beginning nor end; a ray has only a beginning but no end, while 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) having one common point are not located on the same straight line represent a broken line.

The polyline 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, an open one.

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Despite the fact that geometry is one of the exact sciences, scientists cannot unambiguously define the term "straight line". In its most general form, one can give the following definition: "A straight line is a line along which the path is equal to the distance between two points."

What is a straight line in mathematics? Definition of a straight line in mathematics: a straight line has no ends and can continue in both directions to infinity.

The basic concepts of geometry include point, line and plane, they are given without definition, but definitions of other geometric shapes are given through these concepts. A plane, like a straight line, is a primary concept that has no definition. This statement is established by the following axiom: if two points of a line lie in a certain plane, then all points of this line lie in this plane. And the statement itself, which is proved, is called a theorem. The statement of the theorem usually consists of two parts.

Task: where is the line, ray, segment, curve? The tops of the polyline (similar to the tops of mountains) are the point from which the polyline begins, the points at which the segments forming the polyline are connected, the point where the polyline ends. Task: which polyline is longer and which has more vertices? Adjacent sides of a polygon are adjacent links of a broken line. The vertices of the polygon are the vertices of the polyline. Neighboring vertices are endpoints of one side of the polygon.

In mathematics lessons, you can hear the following explanation: a mathematical segment has a length and ends. A segment in mathematics is a set of all points lying on a straight line between the ends of a segment.

In the future, there will be definitions for different figures except for two - a point and a line. So sometimes we can designate a straight line with two capital Latin letters, for example, a straight line\(AB\), since no other straight line can be drawn through these two points. We symbolically write the segment \(AB\).

What is a point in mathematics?

Theorem: The midline of a triangle is parallel to one of its sides and equal to half of that side. C. The height of a right triangle drawn from the vertex of the right angle divides the triangle into two similar right triangles, each of which is similar to the given triangle. C. An inscribed angle based on a semicircle is a right angle. Here are collected the main definitions, theorems, properties of figures on the plane.

The vector with the coordinates of the point is called the normal vector, it is perpendicular to the line.

In a systematic exposition of geometry, a straight line is usually taken as one of the initial concepts, which is only indirectly determined by the axioms of geometry.

4. Two non-coinciding straight lines in a plane either intersect at a single point, or they are parallel. A ray is a part of a straight line bounded on one side. A segment, like a straight line, is indicated by either one letter or two. In the latter case, these letters indicate the ends of the segment.

Summary of the lesson in mathematics

Topic:"Straight. Line designation»

Class: 1 "G"

Lesson Objectives:

Educational:- know the concepts of straight and indirect lines; be able to draw a straight line; be able to distinguish between straight and indirect lines; be able to accept and retain the learning task; be able to perform educational and cognitive actions in material and mental form; be able to work in pairs; the ability to draw conclusions;

Developing:- develop observation, logical thinking, self-control skills; mental operations (analysis, synthesis, generalization); develop the skill of correct speech behavior;

Nurturing: value attitude to the subject, to cultivate attentiveness, accuracy, perseverance, diligence; positive attitude towards learning; desire to acquire new knowledge;

Lesson type: learning new material

Technical support: computer, multimedia projector, screen, interactive whiteboard

Equipment:, textbook "Mathematics 1st grade", workbook in mathematics

UMC:"Perspective"

The date of the: 01.10.2016

Time spending: 45 minutes

Conductive: Boldueva Ludmila Yurievna

Organizing time

Knowledge update

goal setting

Introduction to new material.

Physical education minute

Anchoring

Physical education for the eyes

Anchoring

Outcome

Reflection

10. Homework

Hello, have a seat.

First, let's do an oral count.

Maple leaves (or any other visualization) are attached to the board one at a time, at the expense of the children.

Well done!

Now list the numbers in descending order.

Okay, well done!

Guys, we ended up in the country "Geometry" and we are met by a dot. (teacher pins the first dot on the board). Let's call it point A.

Now with the help of a ruler I will draw a line. Who knows what it's called?

What will be the topic of our lesson?

What will we do today, what will we learn?

Okay, well done!

Video viewing.

So, how many lines can we draw through one point?

We open the textbook on page 50 and look at exercise 1. This shows how a straight line is drawn through one point using a ruler.

Is it possible to draw a line through point A?

We continue, a friend came to visit our point. This is point B. (the teacher attaches point B to the board)

Video viewing.

How many lines can be drawn through two points?

Correctly!

We open workbooks on page 38, perform task 1.

Landing check. Remind how to hold a pencil.

Two points A and B are given. We draw a straight line using a ruler. We mark point O on it. - - What straight lines have we got?

How else can you denote the line AB?

That's right, BA.

(the teacher performs all actions on the interactive whiteboard)

Interactive whiteboard game(2)

But there are also indirect lines, look at the second picture in the tutorial. These are not straight lines. And on the board we have a straight line and an indirect line.

(the board shows a straight line and an indirect line)

And who can say with the help of what we can find out a straight line or not?

That's right, with a ruler. If the ruler coincides with a straight line, then the line is straight, if not, then it is not straight.

Let's try (the teacher applies the ruler to 1 straight line - the ruler coincides, then the line is straight; apply to the second - it does not match, then the line is indirect)

Interactive whiteboard game(1)

Back to workbook number 2, we do it in pairs and then check together. You need to draw straight lines DE and MK, then draw more straight lines through points E, M, K. See. Think with your desk mate and write down the names of these lines.

Checking the completed task. (The teacher draws straight lines on the interactive whiteboard, discussing the correct execution with the children)

On a computer (presentation)

We return to the workbooks and perform number 3.

(the teacher draws with the children on the interactive whiteboard)

Finger gymnastics:

Fingers.

One, two, three, four, five (Squeeze and unclench fists.)

We went for a walk in the woods.

This finger along the path, (Fingers are bent, starting with the big one.)

This finger is on the path,

This mushroom finger

This finger is for raspberries,

This finger is lost

Returned very late.

We stretched our fingers and now we are doing number 4.

Landing rules.

Well, they showed how we hold a pen? Okay, well done!

And the last exercise that we will do in this lesson number 6.

Let's sort it out, we need to find out which of the artists will perform next, if he is not on skates, not a clown and not a bird.

Who fits this description?

That's right, well done!

This is the end of our lesson with you.

What new have we learned today?

What have you learned?

Today at the lesson everyone worked actively, behaved well, and therefore I will now give you the sun.

Guys, raise your hands, those who understood everything in the lesson, easily coped with all the tasks.

And now those who had difficulties.

(And what exactly did you not understand that you did not succeed?)

At home, if you wish, you can do number 7, in the textbook. Here, patterns and numbers need to be redrawn in a notebook.

Hello, sit down.

Together with the teacher, they count the sheets.

Straight line and its designation

Learn to draw a straight line

Working with the textbook

Only one.

Step out and do the job

Spend children, to the music

Working with workbooks

Work in pairs

Perform an exercise

Clenching and unclenching fists

I bend my fingers, I start with a big one

Children's answers

We learned what a straight line is, its name.

Learned how to draw a straight line

Motivational basis of educational activity (L);

Meaning formation (L);

Setting a cognitive goal (P);

Cognitive initiative (P);

Forecasting (P);

educational and cognitive interest (L);

Meaning formation (L);

Volitional self-regulation (P);

Analysis, synthesis, comparison,

generalization, analogy (P);

Statement and formulation

problems (P);

Accounting for different opinions

coordination in

cooperation

different positions (K);

Formulation and argumentation

their opinions and positions in

In geometry, the main geometric figures are the point and the line. To designate points, it is customary to use uppercase Latin letters: A, B, C, D, E, F .... To designate straight lines, lowercase Latin letters are used: a, b, c, d, e, f .... The figure below shows a straight line a, and several points A, B, C, D.

To depict a straight line in the figure, we use a ruler, but we do not depict the entire line, but only a piece of it. Since the line in our view extends to infinity in both directions, the line is infinite.

In the figure above, we see that points A and C are located on a straight line. a. In such cases, we say that the points A and C belong to the line a. Or they say that the line passes through points A and C. When writing, the belonging of a point to a line is indicated by a special icon. And the fact that the point does not belong to the line is marked with the same icon, only crossed out.

In our case, the points B and D do not belong to the line a.

As noted above, in the figure, points A and C belong to the line a. The part of a line that consists of all points on that line that lie between two given points is called segment. In other words, a segment is a part of a straight line bounded by two points.

In our case, we have a segment AB. Points A and B are called the ends of the segment. In order to designate a segment, its ends are indicated, in our case, AB. One of the main properties of membership of points and lines is the following property: through any two points you can draw a line, and moreover, only one.

If two lines have a common point, then the two lines are said to intersect. In the figure, lines a and b intersect at point A. Lines a and c do not intersect.

Any two lines have only one common point or no common points. If we assume the opposite, that two lines have two points in common, then two lines would pass through them. But this is impossible, since only one line can be drawn through two points.