On the this lesson consider the most important practical action in geometry - the measurement of segments. Let us first recall the definitions of a segment and equal geometric figures. Let us introduce the concepts of the length of a segment, the measurement of a segment, and the unit of measurement. Let's talk about basic units measurements and measuring instruments. At the end of the lesson, we will solve several examples for comparing and measuring segments.

If you have difficulty understanding the topic, we recommend that you look at the lessons and,

From the material of the previous lesson, recall what is called a segment. This is geometric figure, which is a part of a straight line between two points. We also figured out how segments are compared - by imposition. However this way comparisons are inconvenient in the case when the segments are very long. In addition, we need to know how different these or those segments are.

Consider Figure 1.

Rice. 1. Segment MN

Segment MN = 2 cm. This entry indicates that there is a reference segment 1 centimeter, which is placed in the segment MN 2 times. A positive number is attached to the segment, which characterizes the length of the segment. The units of measurement for segments are meters, kilometers, centimeters, decimeters and millimeters. Consider the relationship between these units. 1 km = 1000 m. 1m = 10 dm = 100 cm = 1000 mm.

Rice. 2. The sum of the lengths of the segments

In the case when we know the lengths of the segments that are part of this segment, then we can add these lengths and get the total length of the whole segment.

Let's consider some tasks.

On the line AB, mark point C, which lies two centimeters from point A.

Let's make an explanatory drawing.

Rice. 3. Drawing for example 1

The figure shows points that lie at a distance of 2 centimeters from point A, -. It is quite logical that there are 2 such points, because we must take into account 2 centimeters to the right and 2 centimeters to the left.

Point B divides segment AC into 2 parts, the lengths of which are 7.8 cm, 25 mm. Find the length of segment AC.

In Figure 4, these points are marked:

Rice. 4. Drawing for example 2

According to the rule of adding segments AB + BC = AC. However, the complexity of this task lies in the units of measurement, since they are different in the condition. Let 7.8 cm = 78 mm.

In this case, AB + BC = 78 mm + 25 mm = 103 mm = 10.3 cm.

Answer: AC \u003d 103 mm 10.3 cm.

Points B, D, M lie on a straight line. The distance between points B and D is 7 cm, and the distance between D and M is 16 cm. Indicate the distance between points B and M.

Let's consider 2 cases.

Rice. 5. Drawing for example 3

If the point M lies to the right of points B and D, the distance VM can be easily found by the rule of adding the lengths of the segments. VM \u003d BD + DM \u003d 7 + 16 \u003d 23 (cm).

In the case when point M lies to the left of points B and D, then the distance MB is calculated as follows: MB \u003d MD - BD \u003d 16 - 7 \u003d 9 (cm).

Answer: 23 cm or 9 cm.

On the segment AB with a length of 64 cm, the middle C is marked. On the ray CA, the point D is marked, the distance from which to the middle is 15 cm. Find the length of the segments DB and DA.

Let's draw a picture for the problem.

Rice. 6. Drawing for example 4

Since C is the middle of the segment AB, then the segment AC \u003d CB \u003d 64: 2 \u003d 32 (cm). It is important to point out that the position of the point D is unique. Let's find the segments indicated in the condition: DВ \u003d CB + DC \u003d 32 + 15 \u003d 47 (cm). DA \u003d AC - DC \u003d 32 - 15 \u003d 17 (cm).

Answer: 47 cm, 17 cm.

Do points A, B and C lie on the same straight line if AB = 3 cm, CB = 4 cm, AC = 5 cm?

Recall that in the case when three points lie on one straight line, the larger segment is equal to the sum two others. For example:

Rice. 7. Drawing for example 5

If AC = AB + BC is satisfied, then the three points A, B and C lie on the same straight line. In our case, the length of segment AC is not equal to the sum of segments AB and CB, since 3 + 4 = 7 5.

Therefore, these three points will form a triangle:

Rice. 8. Drawing for example 5

Answer: Points A, B, C do not lie on a straight line.

1. Alexandrov A.D., Werner A.L., Ryzhik V.I. etc. Geometry 7. - M.: Enlightenment.
2. Atanasyan L.S., Butuzov V.F., Kadomtsev S.B. et al. Geometry 7. 5th ed. - M.: Enlightenment.
3. Butuzov V.F., Kadomtsev S.B., Prasolova V.V. Geometry 7 / V.F. Butuzov, S.B. Kadomtsev, V.V. Prasolova, ed. Sadovnichy V.A. - M.: Education, 2010.

1. Measurement of segments ().
2. General lesson on geometry in the 7th grade ().
3. Straight line, segment ().

1. No. 7, 8. Butuzov V.F., Kadomtsev S.B., Prasolova V.V. Geometry 7 / V.F. Butuzov, S.B. Kadomtsev, V.V. Prasolova, ed. Sadovnichy V.A. - M.: Education, 2010.

2. Indicate whether points A, B and C lie on the same line if AC = 2 cm, BC = 8 cm, BA = 4 cm.

3. Indicate what the length of the segment ME is equal to if the segment AK \u003d 2 cm, and K, M, R are the midpoints of the segments.

4.* The perimeter (the sum of all sides) of the rectangle is 36 cm, and the longest side is 12 cm. Find the smaller side rectangle.

Straight

The concept of a line, as well as the concept of a point, are the basic concepts of geometry. As you know, the basic concepts are not defined. This is no exception to the concept of a straight line. Therefore, let us consider the essence of this concept through its construction.

Take a ruler and, without lifting your pencil, draw a line of arbitrary length (Fig. 1).

We will call the resulting line straight. However, it should be noted here that this is not the entire line, but only part of it. It is not possible to construct the whole straight line, it is infinite at both its ends.

Straight lines will be denoted by small Latin letter, or two of its points in parentheses(Fig. 2).

The concepts of a line and a point are connected by three axioms of geometry:

Axiom 1: For every arbitrary line, there are at least two points that lie on it.

Axiom 2: It is possible to find at least three points that will not lie on the same line.

Axiom 3: Through $2$ arbitrary points always passes through a line, and this line is unique.

For two straight lines, their relative position is relevant. Three cases are possible:

1. The two lines are the same. In this case, each point of one will also be a point of the other line.
2. Two lines intersect. In this case, only one point from one line will also belong to the other line.
3. Two lines are parallel. In this case, each of these lines has its own set of points distinct from each other.

In this article, we will not dwell on these concepts in detail.

Line segment

Let us be given an arbitrary line and two points belonging to it. Then

Definition 1

A segment will be called a part of a straight line, which is limited by its two arbitrary different points.

Definition 2

The points by which the segment is bounded within the framework of Definition 1 are called the ends of this segment.

The segments will be denoted by its two endpoints in square brackets(Fig. 3).

Segment comparison

Consider two arbitrary segments. Obviously, they can be either equal or unequal. To understand this, we need the following axiom of geometry.

Axiom 4: If both ends of two different segments coincide when they are superimposed, then such segments will be equal.

So, to compare the segments we have chosen (let's designate their segment 1 and segment 2), let's put the end of segment 1 on the end of segment 2, so that the segments remain on one side of these ends. After such an overlay, there are two possible following cases:

Cut length

In addition to comparing segments with others, it is also often necessary to measure segments. To measure a line means to find its length. To do this, you need to select some kind of "reference" segment, which we will take as a unit (for example, a segment whose length is 1 centimeter). After choosing such a segment, we compare the segments with it, the length of which must be found. Consider an example.

Example 1

Find the length of the next segment

if the next segment is 1

To measure it, we take the segment $$ as a standard. We will postpone it to the segment $$. We get:

Answer: $6$ cm.

The concept of the length of a segment is associated with the following axioms of geometry:

Axiom 5: By choosing a certain unit of measure for segments, the length of any segment will be positive.

Axiom 6: By choosing a certain unit of measurement for segments, we can find, for any positive number, a segment whose length is equal to the given number.

After determining the length of the segments, we have a second way to compare the segments. If, with the same choice of the length unit, the segment $1$ and the segment $2$ will have the same length, then such segments will be called equal. If, without loss of generality, segment 1 will have a length of numerical value less than the length of the segment $2$, then the segment $1$ will be less than a segment $2$.

by the most in a simple way measuring the length of line segments is a measurement, using a ruler.

Example 2

Record the lengths of the following segments:

Let's measure them with a ruler:

1. $4$ see
2. $10$ see
3. $5$ see
4. $8$ see

>>Geometry: Measuring line segments. Complete Lessons

Distance measurement

DI. Mendeleev wrote: Science begins as soon as one begins to measure: exact science unthinkable without measure".

Man is faced with the need to measure ancient times, at an early stage of its development practical life, in agriculture, the construction of their homes, the palaces of their rulers, temples, in trade. People needed to measure distances, areas, volumes, weights, and, of course, time.

The first units of length were very approximate. They were associated with the size of parts of the human body. Units of length are still used in England and the US today" sole" - foot(31 cm), " thumb" - inch(25.4 mm) and yard(91 cm). It was equal to the distance from the tip of the nose of King Henry I to the end of his fingers. outstretched hand. 1ft=12 inches.

The study in the course of mathematics of the school of quantities and their measurements has great importance in terms of development junior schoolchildren. This is due to the fact that through the concept of magnitude, the real properties of objects and phenomena are described, the knowledge of the surrounding reality takes place; acquaintance with the dependencies between quantities helps to create in children holistic ideas about the world around them; the study of the process of measuring quantities contributes to the acquisition practical skills and skills necessary for a person in his daily activities. In addition, knowledge and skills related to quantities and obtained in primary school, are the basis for further study of mathematics.

VALUE- This special property real objects or phenomena, and the peculiarity lies in the fact that this property can be measured, that is, to name the number of quantities that express the same property of objects, are called quantities of the same kind or homogeneous quantities.
For example, the length of the table and the length of the rooms are homogeneous values.
Quantities - length, area, mass and others have a number of properties.

• Any two quantities of the same kind are comparable: they are either equal, or one smaller(more) another. That is, for quantities of the same kind, the relations " equals», « smaller», « more» and for any quantities and one and only one of the following relations is true: For example, we say that the length of the hypotenuse right triangle more than any cathet given triangle; the mass of a lemon is less than the mass of a watermelon; length opposite sides rectangles are equal.
• Values ​​of the same kind can be added, and the result of the addition is a value of the same kind. Those. for any two values ​​a and b, the value a + b is uniquely determined, it is called the sum of the values ​​a and b. For example, if a is the length of segment AB, b is the length of segment BC, then the length of segment AC is c, which is the sum of the lengths of segments AB and BC. (Fig.1)

• The value is multiplied by real number, resulting in a quantity of the same kind. Then for any value a and any non-negative number x there is a single value b = x a, the value b is called the product of the value a and the number x. For example, if a is the length of the segment AB multiplied by x = 2, then we get the length of the new segment AC. (Fig. 2)

(Fig.2)

• Values ​​of this kind are subtracted by determining the difference of values ​​through the sum: the difference between the values ​​of a and b is such a value c that a=b+c. For example, if a is the length of segment AB, b is the length of segment BC, then the length of segment BC is the difference between the lengths of segments AC and AB. (Fig.1)
• Values ​​of the same kind are divided, defining the quotient through the product of the value by the number; private quantities a and b is a non-negative real number x such that a = x b. More often, this number is called the ratio of the values ​​\u200b\u200bof a and b and is written in this form: a / b \u003d x. For example, the ratio of the length of segment AC to the length of segment AB is 2. (Fig. 2).

Cut length is uniquely defined and is non-negative number, equal to the distance between its end points.
Now is the time to recall four definitions that will help us understand how to measure segments.

1. If point A is located on a marked line, which in this case is called a "number line" (for example, a ruler), then the number corresponding to this point is called its coordinate.
2. The distance between points A and B on a straight line is the modulus of the difference between their coordinates.
3. The length of the segment defined by A and B is the modulus of the difference between the coordinates of points A and B.
4. Two segments are equal if they have the same length.

Let segment AB be given. If we consider the ruler as part of the number line and arrange AB along the ruler so that point A coincides with zero, then point B will be located opposite the number equal to the length of AB. The length of AB is denoted by AB.
From the definitions, you should know that if none of the ends of the segment coincides with zero, then to calculate the length of the segment, you need to find the modulus of the difference in the coordinates of the end points.
When measuring the length of a segment, we assume that it is uniquely defined. That is, there is singular on the number line such that if one of the ends of the segment is aligned with zero, then the second will coincide with this number. This assumption is justified by the following axioms.
The distance between two points A and B on the number line is uniquely defined.

If one of the ends of the given segment coincides with zero, then the coordinate of the second is determined in a unique way.

The following axiom allows us to add the lengths of two segments to get the length of the third.

If point Q is located between points A and B, then the sum of the lengths of AQ and QB equals the length of AB.

A point P lying between points A and B is called the midpoint of segment AB if AP = PB.
The middle of the segment is unique.

Measure segment- this means to set its length in certain units. Length units: millimeter (mm), centimeter (cm), decimeter (dm), meter (m), kilometer (km). Between units of length (single segments) the following relation is accepted:

• 1 cm - 10 mm;
• 1 dm - 10 cm - 100 mm;
• 1 m - 10 dm - 100 cm - 1000 mm;
• 1 km - 1000 m.

The most common tools for measuring line lengths are: ruler(with markings in centimeters and millimeters) and roulette(with centimeter, decimeter and meter markings). To build segments, students use rulers with millimeter and centimeter markings.
To build a segment of a given length, you need to combine the start point of the segment and the number 0 on the ruler. Then, on the marking scale on the ruler, you need to find the length of the segment and mark the end point of the segment. The beginning and end of the segment are connected with a pencil, without removing the ruler.
segment of a given length

On this ruler, the numbers indicate the number of segments in centimeters (single segments of 1 cm), small divisions are single segments of 5 mm. The length of the constructed segment is 50 mm, or 5 cm 0 mm.

Crossword

Horizontally:
1. A beam dividing the angle in half.
4. Triangle element.
5, 6, 7. Views of a triangle (at the corners).
11. Mathematician of antiquity.
12. Part of the line.
15. Side of a right triangle.
16. A segment connecting the vertex of a triangle with the midpoint of the opposite side.

Vertically:
2. Top of the triangle.
3. Figure in geometry.
8. Triangle element.
9. View of a triangle (on the sides).
10. A segment in a triangle.
13. A triangle whose two sides are equal.
14. Side of a right triangle.
17. Triangle element.

Answers:
Horizontally:
1. Bisector.
4. Party.
5. Rectangular.
6. Acute-angled.
7. Obtuse.
11. Pythagoras.
12. Cut.
15. Hypotenuse.
16. Median.

Vertically:
2. Point.
3. Triangle.
8. Top.
9. Equilateral.
10. Height.
13. Isosceles.
14. Leg.
17. Angle.

Questions:

1. What did people measure in ancient times?
2. Name the units of length in England and the USA.
3. What is the length of a segment?
4. What is 1 decemeter equal to?
5. Name the devices for measuring length.

Introduce students to the procedure for measuring segments, consider the properties of segment lengths, introduce various units of measurement and tools for measuring segments,

Develop the ability to measure without tools.

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MBOU "Apraksinskaya secondary school"

Related lesson

“Measurement of segments”

(geometry, grade 7)

(with presentation)

Prepared and hosted: Alyakina E.I.

2017

Development of a geometry lesson in grade 7.

Lesson topic: Distance measurement

Goals:

• Introduce students to the procedure for measuring segments, consider the properties of segment lengths, introduce various units of measurement and tools for measuring segments,
• Develop the ability to measure without tools.

Equipment: computer, projector, screen; rulers, compasses, tape measure.

The lesson is accompanied by a presentation

During the classes

1. Organizational moment. slide 1

2. Actualization of knowledge. front poll. slide 2

1. How many lines can be drawn through two points?

2. How much common points can have two straight lines?

3. Explain what a cut is.

4. Explain what a ray is. How are rays defined?

5. What shape is called an angle? Explain what a vertex and sides of an angle are.

6. What angle is called a turned angle?

7. What figures are called equal?

8. Explain how to compare two segments?

9. What point is called the midpoint of the segment?

10. Explain how to compare two angles?

11. Which ray is called the angle bisector?

3. Motivation for activity. Definition of the topic and purpose of the lesson.

slide 3

One medieval philosopher Marsilio Sicino said:« Measure yourself - and you will become a real geometer!How do you understand this statement?(Discussion)

Each person repeatedly had to measure something: the height of a tree, its own weight, the length of the jump, speed, and much more. From the point of view of geometry, in such cases we deal with the measurement of segments.

slide 4

Recording the topic of the lesson:Distance measurement

slide 5

Goal setting:get acquainted with the procedure for measuring segments, consider the properties of segment lengths, get acquainted with various units of measurement for length and tools for measuring segments, learn how to measure without tools.

Measurements are made in certain units: length - measured in units of length, weight - in units of weight, etc.

slide 6

What does it mean to measure something?

This means - to compare it with a certain standard.

A measurement is a comparison of a measurement object with a selected unit of measurement.

Slide 7

As you know, the characters of one cartoon measured the length of a boa constrictor in parrots. For the inhabitants rainforest, in which the parrot lives, this unit is no worse than others. But the length in parrots will not tell the inhabitants of the taiga anything.

Slide 8

This cartoon story is not so ridiculous. Rulers different countries liked to establish their measures, often associated with their own person.

Slide 9

For example, English King Henry Iintroduced as units of length YARD - the distance from the tip of his nose to thumb outstretched hand.

More democratic in origin is the other English unit FT length, which means "foot" in English. 16 Englishmen lined up in a chain in such a way that each next one touched the heels of the previous one with the ends of their toes. 1/16 of such a chain was 1 foot.

Slide 10

In Russia in the old days, the measure of length was STEP, SPAN: small span equal to the distance between the ends of the stretched fingers, thumb and index (~ 19 cm), big span - the distance between the extended thumb and little finger (~ 23 cm),

slide 11

PALM - the width of the hand, ELBOW - the distance from the elbow to the end of the middle finger.

slide 12

Long distances were measured by the FLIGHT OF THE ARROW.

A little later, ARSHIN appeared, from Persian - cubit (~ 71 cm), there was a Persian arshin, Turkish arshin, etc., hence the saying "Measure on your own arshin" appeared.

Arshin was divided into 16 inches,

slide 13

3 arshins made up a FATCH - the distance from the foot to the end of the middle finger of an outstretched hand, 500 fathoms - made up a VERST (or field), 7 versts - a MILE.

Slide 14

With the development of production and trade, people became convinced that it is not always convenient to measure distances with steps or elbows, since the length of an elbow or a step is different people different, and the measure of length must be constant. This is how the meter was born.

The meter, adopted as a standard, is now stored in one of the French museums.

So what does "measure" mean?

slide 15

In short, you can answer like this: “To measure means to compare with the standard.”

4. Tools

slide 16

What do we usually measure? Comparing?

The oldest geometric tools arecompass and ruler. First, a ruler was invented, and the compass was invented much later. The figures of the papyrus of Ahmes, for example, testify to the use of a ruler, but not a compass. The compass was invented in Ancient Greece.

Slide 17

In technical drawing, a scale millimeter ruler is used. A caliper is used to measure the tube diameter.

Slide 18

A tape measure is used to measure distances on the ground.

"Roulette" - a term French descent(rouler - roll, roll).

5. Properties of the length of a segment.

Slide 19

Let's try to figure out some properties of length.

1. What segments cannot be drawn? a) 2.5 cm, b) 7 cm, c) - 4 cm.

The length of the segment is expressed positive number.

2. What can be said about the length of two equal segments?

equal segments have equal lengths.

3. If you draw a segment AB, put a point C on it, you will get segments AC and CB. What can you learn by adding the lengths of the segments AC and CB?

The length of the entire segment is equal to the sum of the lengths of the segments of which it consists.

6. Problem solving

Slide 20

We will solve several problems for measuring segments.

1) (oral) On the KM segment, a point O was set, KO = 7.9dm, OM = 4.5dm. Find the length of KM.

2) (in writing) Point C lies on the segment AB, AC \u003d 3.6 cm, AB \u003d 9.8 cm. Find the length of CB.

slide 21

Sample design

slide 22

3) (orally) Determine the length of the segment MN if LN=7.6cm.

4. (oral) Segment BC = 7m and PK = 0.8BC, Find the length of the segment PK.

5. (oral) Cut DE = 13mm and DE = 0.1RT. Find RT.

slide 23

Decide on your own

1) The point M lies on the line EF between E and F. What is the length of the segment MF if EF = 8.3cm, EM = 3.3cm? (The decision is drawn up according to the model of the previous one) Answer: MF=5cm.

2) Segment AI, the length of which is 8 dm, is divided into equal parts. Find the length of segment DH. Answer: DH=4dm.

3) Points K and R lie on the segment LS so that K lies between L and R,

LK=5.2cm, LS=18cm and LK=KR. Find RS. (The teacher checks the solution and design of each) Answer: RS=7.6cm.

slide 24

solve problems

6. Points A, B and C lie on the same straight line. It is known that AB=9cm, BC=11.5cm.

What is the length of segment AC?

Answer: AC=20.5cm or AC=2.5cm

7. AC=10mm, BD=14mm, AD=16mm. Find the sun

Answer: BC=8mm.

8. AB=4.6m, BC=9.26m, DA=24.76m. Find a CD

Answer: CD=10.9m

8. Practical work"Live meter".

Please note: for measuring small distances, you should remember the length between the ends of the spaced thumb and little finger. You should know the greatest distance between the ends of the index and middle fingers. Finally, you need to know the width of your fingers, the length of the foot, the span of the arms.

Measure following distances and write it down in your notebook.

1. span - the distance between the ends of the stretched fingers, thumb and index (~ 19 cm),
2. elbow - the distance from the elbow to the end of the middle finger (~ 71 cm).
3. oblique sazhen (248cm) - the distance from the toes of the left foot to the end of the toes of the raised right hand,
4. fly fathom (176cm) - the distance between the ends of the fingers of the hands spread apart
5. foot (foot), height, belt length, etc.

Now let's measure the objects around us (optional: the length, width and height of the desk, notebook, blackboard, classroom etc.) in three ways:

1. First, we determine the length "by eye" without measuring instruments;
2. Then we measure, knowing the "own" lengths of body parts;
3. Let's check with the help of measuring tools how wrong we are.

Discussion.

Guys, it is useful to be able not only to measure distances without a measuring ruler, in steps, but also to evaluate them directly by eye. This skill can only be developed through practice.

Try, having gone out with your comrades on the road, outline some roadside object and figure out how many steps are up to it. Then count the steps to determine whose score is closer to the true one wins.

9. The result of the lesson. Reflection

- What new did you learn today?

Slide 25

Did we achieve the goal of the lesson?

Slides 26, 27, 28

And now the mini-test "Complete the sentences."

What knowledge learned in class can you apply in your life?

Slide 29

10. Homework.Grading.

pp. 7-8 (pp. 13-16), #24, #25, #32, #33.

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Slides captions:

“Inspiration is needed in geometry no less than in poetry” A.S. Pushkin

1. How many lines can be drawn through two points? 2. How many common points can two lines have? 3. Explain what a segment is. 4. Explain what a beam is. How are rays defined? 5. What figure is called an angle? Explain what a vertex and sides of an angle are. 6. What angle is called deployed? 7. What figures are called equal? 8. Explain how to compare two segments? 9. What point is called the midpoint of the segment? 10. Explain how to compare two angles? 11. Which ray is called the angle bisector? Oral survey:

Marsilio Sicino Measure yourself and you will become a real geometer.

Measurement of segments Geometry - 7kl. Measure what is measurable and make what is not measurable accessible.” G. Galileo

Purpose: to get acquainted with the procedure for measuring segments, to consider the properties of segment lengths, to get acquainted with various units of length measurement, to get acquainted with tools for measuring segments, to learn how to measure without tools.

ASK YOURSELF THE QUESTION: “What does it mean to measure some value? “It means to compare it with a certain standard. A measurement is a comparison of a measurement object with a selected unit of measurement.

In parrots, the length of the boa constrictor was 38 parrots, in monkeys - 5 monkeys, and in baby elephants - only 2 baby elephants. Naturally, the boa constrictor liked the fact that it was longer in parrots. So in the measurement it is very important to choose the unit of measure. good performance about the measurement gives a cute cartoon "38 parrots". It solved the problem of measuring the length of a boa constrictor. If you need to measure the length of two boas, then both must be measured either in parrots, or in monkeys, or in baby elephants. "38 parrots"

Units of measurement from antiquity to the present day The first units of length were approximate. They were associated with the size of parts of the human body. Science begins as soon as one begins to measure. DI. Mendeleev

And the English king Henry I introduced the YARD as units of length - the distance from the tip of his nose to the thumb of his outstretched hand. Units of measurement from antiquity to the present day Another English unit of length is the FUT, which in English means "foot". 16 Englishmen lined up in a chain in such a way that each next one touched the heels of the previous one with the ends of their toes. 1/16 of such a chain was 1 foot.

In Russia, in the old days, the measure of length was STEP and SPAN: the small span was equal to the distance between the ends of the extended fingers, the thumb and the index finger (~ 19 cm), the large span was the distance between the spread thumb and little finger (~ 23 cm) Units of measurement from antiquity to ours days

Units of measurement from antiquity to the present day PALM - the width of the hand, ELBOW - the distance from the elbow to the end of the middle finger (~ 71 cm).

Arshin in Persian means elbow. There was a Persian arshin, a Turkish arshin, etc., hence the saying “Measure on your own arshin” appeared. Long distances were measured by the FLIGHT OF THE ARROW. Units of measurement from antiquity to the present day

3 arshins made SAZHEN Units of measurement from antiquity to the present day B Ancient Russia as units of measurement of length were used: oblique fathom (248 cm) - the distance from the toes of the left foot to the end of the fingers of the raised right hand, fly fathom (176 cm) - the distance between the ends of the fingers of the arms spread apart, the elbow (45 cm) - the distance from the ends of the fingers to elbow of bent arm.

The length of the elbow or step is different for different people, and the measure of length should be the same. a meter appeared Units of measurement from antiquity to the present day A sample of a measure - a meter, accepted as a standard, is now stored in one of the French museums.

Let's return to the question asked at the beginning: "What does it mean to measure?" In short, you can answer like this: “To measure means to compare with the standard.” Units of measurement from antiquity to the present day

Tools The most ancient geometrical tools include compasses and a ruler. First, a ruler was invented, and the compass was invented later - in the 1st century in Ancient Greece. What do we usually measure?

In technical drawing, a scale millimeter ruler is used. Instruments A caliper is used to measure the tube diameter.

A tape measure is used to measure distances on the ground. "Roulette" - from French (rouler - roll, roll). Instruments

Line length properties 1. Which line segments cannot be drawn? a) 2.5 cm, b) 7 cm, c) - 4 cm Conclusion 1: the length of the segment is expressed as a positive number. 2. What can be said about the length of two equal segments? Conclusion 2: equal segments have equal lengths. 3. If you draw a segment AB, put a point C on it, you will get segments AC and CB. What can you learn by adding the lengths of the segments AC and CB? Conclusion 1: the length of the entire segment is equal to the sum of the lengths of the segments of which it consists.

Problem solving 1. (oral) A point O is set on the KM segment, KO = 7.9 dm, OM = 4.5 dm. Find the length of KM. 2. (in writing) Point C lies on segment AB, AC \u003d 3.6 cm, AB \u003d 9.8 cm. Find the length of CB.

2. Point C lies on the segment AB, AC \u003d 3.6 cm, AB \u003d 9.8 cm. Find the length of CB. Given: segment AB, C AB, AC \u003d 3.6 cm, AB \u003d 9.8 cm. Find: SV. Decision. CB = AB - AC, CB = 9.8 - 3.6 = 6.2 (cm). Answer: SW = 6.2 cm. Sample design

4. (oral) Segment BC = 7m and PK = 0.8BC, Find the length of the segment PK. Problem solving 3. (oral) Determine the length of the segment NM if LN = 7.6 cm. 5. (oral) The segment DE = 13 mm and DE = 0.1RT. Find RT.

Solve it yourself 1. Point M lies on the line EF between E and F. What is the length of segment MF if EF = 8.3cm, EM = 3.3cm? 2. Segment A I, the length of which is 8 dm, is divided into equal parts. Find the length of the segment DH . 3. Points K and R lie on the segment LS so that K lies between L and R, LK = 5.2 cm, LS = 18 cm and LK = KR. Find RS. Answer: MF = 5 cm. Answer: DH = 4dm. Answer: RS = 7.6 cm.

7. AC=10mm, B D=14mm, A D=16mm. Find the sun. Problem solving 6. Points A, B and C lie on the same line. It is known that AB \u003d 9 cm, BC \u003d 11.5 cm. What can be the length of the segment AC? 8. AB=4.6m, BC=9.26m, DA=24.76m. Find CD. Answer: AC=20.5cm or AC=2.5cm. Answer: BC=8mm. Answer: CD \u003d 10.9 m.

get acquainted with the procedure for measuring segments, consider the properties of segment lengths, get acquainted with various units of measurement for length and tools for measuring segments, learn how to measure without tools. Let's go back to the purpose of the lesson

Complete sentences 1. English king Henry I introduced YARD as units of length - the distance from ... the tip of his nose to the thumb of an outstretched hand. 2. FOOT, which in English means ... “foot” 3. ELBOW is approximately equal to ... 71 cm 4. FLYING FATHOUSE - the distance between ... arms extended to the sides

5. The length of the segment is expressed by ... a positive number 6. Equal segments have ... equal lengths 7. The length of the entire segment is equal to the sum of the lengths of the segments of ... of which it consists 8. The standard of the meter is stored in ... one of the French museums 9. To measure means to compare with ... standard Complete the sentences

10. The oldest geometric tools include ... a compass and a ruler, a millimeter ruler, a vernier caliper, a tape measure 11. In technical drawing, they use a scale ... 12. To measure the diameter of a tube, use ... 13. To measure distances on the ground, they use ... Complete the sentences