Construct a triangle symmetrical to the given one about the axis. Math lesson. Topic: "Axis of symmetry"

I . Symmetry in mathematics :

Basic concepts and definitions.

Axial symmetry (definitions, construction plan, examples)

Central symmetry (definitions, construction plan, whenmeasures)

Summary table (all properties, features)

II . Applications of symmetry:

1) in mathematics

2) in chemistry

3) in biology, botany and zoology

4) in art, literature and architecture

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1. Basic concepts of symmetry and its types.

The concept of symmetry R goes back through the entire history of mankind. It is found already at the origins of human knowledge. It arose in connection with the study of a living organism, namely man. And it was used by sculptors back in the 5th century BC. e. The word “symmetry” is Greek and means “proportionality, proportionality, sameness in the arrangement of parts.” It is widely used by all areas of modern science without exception. Many great people have thought about this pattern. For example, L.N. Tolstoy said: “Standing in front of a black board and drawing different figures on it with chalk, I was suddenly struck by the thought: why is symmetry clear to the eye? What is symmetry? This is an innate feeling, I answered myself. What is it based on?” The symmetry is truly pleasing to the eye. Who hasn’t admired the symmetry of nature’s creations: leaves, flowers, birds, animals; or human creations: buildings, technology, everything that surrounds us since childhood, everything that strives for beauty and harmony. Hermann Weyl said: “Symmetry is the idea through which man throughout the ages has tried to comprehend and create order, beauty and perfection.” Hermann Weyl is a German mathematician. His activities span the first half of the twentieth century. It was he who formulated the definition of symmetry, established by what criteria one can determine the presence or, conversely, absence of symmetry in a given case. Thus, a mathematically rigorous concept was formed relatively recently - at the beginning of the twentieth century. It's quite complicated. Let us turn and once again remember the definitions that were given to us in the textbook.

2. Axial symmetry.

2.1 Basic definitions

Definition. Two points A and A 1 are called symmetrical with respect to line a if this line passes through the middle of segment AA 1 and is perpendicular to it. Each point of a line a is considered symmetrical to itself.

Definition. The figure is said to be symmetrical about a straight line A, if for each point of the figure there is a point symmetrical to it relative to the straight line A also belongs to this figure. Straight A called the axis of symmetry of the figure. The figure is also said to have axial symmetry.

2.2 Construction plan

And so, to construct a symmetrical figure relative to a straight line, from each point we draw a perpendicular to this straight line and extend it to the same distance, mark the resulting point. We do this with each point and get symmetrical vertices of a new figure. Then we connect them in series and get a symmetrical figure of a given relative axis.

2.3 Examples of figures with axial symmetry.

3. Central symmetry

3.1 Basic definitions

Definition. Two points A and A 1 are called symmetrical with respect to point O if O is the middle of the segment AA 1. Point O is considered symmetrical to itself.

Definition. A figure is said to be symmetrical with respect to point O if, for each point of the figure, a point symmetrical with respect to point O also belongs to this figure.

3.2 Construction plan

Construction of a triangle symmetrical to the given one relative to the center O.

To construct a point symmetrical to a point A relative to the point ABOUT, it is enough to draw a straight line OA(Fig. 46 ) and on the other side of the point ABOUT set aside a segment equal to the segment OA. In other words , points A and ; In and ; C and symmetrical about some point O. In Fig. 46 a triangle is constructed that is symmetrical to a triangle ABC relative to the point ABOUT. These triangles are equal.

Construction of symmetrical points relative to the center.

In the figure, points M and M 1, N and N 1 are symmetrical relative to point O, but points P and Q are not symmetrical relative to this point.

In general, figures that are symmetrical about a certain point are equal .

3.3 Examples

Let us give examples of figures that have central symmetry. The simplest figures with central symmetry are the circle and parallelogram.

Point O is called the center of symmetry of the figure. In such cases, the figure has central symmetry. The center of symmetry of a circle is the center of the circle, and the center of symmetry of a parallelogram is the point of intersection of its diagonals.

A straight line also has central symmetry, but unlike a circle and a parallelogram, which have only one center of symmetry (point O in the figure), a straight line has an infinite number of them - any point on the straight line is its center of symmetry.

The pictures show an angle symmetrical relative to the vertex, a segment symmetrical to another segment relative to the center A and a quadrilateral symmetrical about its vertex M.

An example of a figure that does not have a center of symmetry is a triangle.

4. Lesson summary

Let us summarize the knowledge gained. Today in class we learned about two main types of symmetry: central and axial. Let's look at the screen and systematize the knowledge gained.

Summary table

	Axial symmetry	Central symmetry
Peculiarity	All points of the figure must be symmetrical relative to some straight line.	All points of the figure must be symmetrical relative to the point chosen as the center of symmetry.
Properties	1. Symmetrical points lie on perpendiculars to a line. 3. Straight lines turn into straight lines, angles into equal angles. 4. The sizes and shapes of the figures are preserved.	1. Symmetrical points lie on a line passing through the center and a given point of the figure. 2. The distance from a point to a straight line is equal to the distance from a straight line to a symmetrical point. 3. The sizes and shapes of the figures are preserved.

II. Application of symmetry

Mathematics	In algebra lessons we studied the graphs of the functions y=x and y=x The pictures show various pictures depicted using the branches of parabolas. (a) Octahedron, (b) rhombic dodecahedron, (c) hexagonal octahedron.
Russian language	The printed letters of the Russian alphabet also have different types of symmetries. There are “symmetrical” words in the Russian language - palindromes, which can be read equally in both directions.	A D L M P T F W– vertical axis V E Z K S E Y - horizontal axis F N O X- both vertical and horizontal B G I Y R U C CH SCHY- no axis Radar hut Alla Anna
Literature	Sentences can also be palindromic. Bryusov wrote a poem “The Voice of the Moon”, in which each line is a palindrome. Look at the quadruples of A.S. Pushkin “ Bronze Horseman" If we draw a line after the second line we can notice elements of axial symmetry	And the rose fell on Azor's paw. I come with the sword of the judge. (Derzhavin) "Search for a taxi" "Argentina beckons the Negro" “The Argentine appreciates the black man,” “Lesha found a bug on the shelf.” The Neva is dressed in granite; Bridges hung over the waters; Dark green gardens Islands covered it...

Biology

The human body is built on the principle of bilateral symmetry. Most of us view the brain as a single structure; in reality, it is divided into two halves. These two parts - two hemispheres - fit tightly to each other. In full accordance with the general symmetry of the human body, each hemisphere is an almost exact mirror image of the other Control of the basic movements of the human body and its sensory functions is evenly distributed between the two hemispheres of the brain. The left hemisphere controls the right side of the brain, and the right hemisphere controls the left side.

Botany

A flower is considered symmetrical when each perianth consists of an equal number of parts. Flowers having paired parts are considered flowers with double symmetry, etc. Triple symmetry is common in monocotyledons, and quintuple symmetry in dicotyledons. Characteristic feature The structure of plants and their development is helicity. Pay attention to the leaf arrangement of the shoots - this is also a peculiar type of spiral - a helical one. Even Goethe, who was not only a great poet, but also a natural scientist, considered helicity one of characteristic features of all organisms, a manifestation of the innermost essence of life. The tendrils of plants twist in a spiral, the growth of tissues in tree trunks occurs in a spiral, the seeds in a sunflower are arranged in a spiral, and spiral movements are observed during the growth of roots and shoots.

A characteristic feature of the structure of plants and their development is spirality. Look at the pine cone. The scales on its surface are arranged strictly regularly - along two spirals that intersect approximately at a right angle. The number of such spirals in pine cones is 8 and 13 or 13 and 21.

Zoology

Symmetry in animals means correspondence in size, shape and outline, as well as the relative arrangement of body parts located on opposite sides of the dividing line. With radial or radial symmetry, the body has the shape of a short or long cylinder or vessel with a central axis, from which parts of the body extend radially. These are coelenterates, echinoderms, and starfish. With bilateral symmetry, there are three axes of symmetry, but only one pair of symmetrical sides. Because the other two sides - abdominal and dorsal - are not similar to each other. This type of symmetry is characteristic of most animals, including insects, fish, amphibians, reptiles, birds, and mammals.

Axial symmetry

	Different kinds symmetry of physical phenomena: symmetry of electric and magnetic fields (Fig. 1) The distribution is symmetrical in mutually perpendicular planes electromagnetic waves(Fig. 2)	Fig.1 Fig.2
Art	Mirror symmetry can often be observed in works of art. Mirror" symmetry is widely found in works of art of primitive civilizations and in ancient paintings. Medieval religious paintings are also characterized by this type of symmetry. One of Raphael’s best early works, “The Betrothal of Mary,” was created in 1504. Under a sunny blue sky lies a valley topped by a white stone temple. In the foreground is the betrothal ceremony. The High Priest brings Mary and Joseph's hands together. Behind Mary is a group of girls, behind Joseph is a group of young men. Both parts of the symmetrical composition are held together by the counter-movement of the characters. For modern tastes, the composition of such a painting is boring, since the symmetry is too obvious.

Chemistry	A water molecule has a plane of symmetry (straight vertical line). DNA molecules (deoxyribonucleic acid) play an extremely important role in the world of living nature. It is a double-chain high-molecular polymer, the monomer of which is nucleotides. DNA molecules have a double helix structure built on the principle of complementarity.
Architeculture	Man has long used symmetry in architecture. The ancient architects made especially brilliant use of symmetry in architectural structures. Moreover, the ancient Greek architects were convinced that in their works they were guided by the laws that govern nature. By choosing symmetrical forms, the artist thereby expressed his understanding of natural harmony as stability and balance. The city of Oslo, the capital of Norway, has an expressive ensemble of nature and art. This is Frogner - a park - a complex of garden and park sculpture, which was created over the course of 40 years.	Pashkov House Louvre (Paris)

© Sukhacheva Elena Vladimirovna, 2008-2009.

• Central symmetry
• Axial symmetry
• Conclusion

Definition

Symmetry (from the Greek Symmetria - proportionality), in a broad sense, is the immutability of the structure of a material object relative to its transformations. Symmetry plays a huge role in art and architecture. But it can be seen both in music and poetry. Symmetry is found widely in nature, especially in crystals, plants and animals. Symmetry can also be found in other areas of mathematics, for example, when constructing graphs of functions.

Central symmetry

Two points A And A 1 are called symmetrical about the point ABOUT, If ABOUT - midpoint AA 1. point ABOUT is considered symmetrical to itself.

Constructing a point centrally symmetrical to a given point

• Build AO beam
• Measure the length of segment AO
• Point A1 is symmetrical to point A relative to center O.

A 1

Construction of a segment centrally symmetrical to a given one

• Build AO beam
• Measure the length of segment AO
• Place a segment OA 1 on the ray AO on the other side of the point O, equal to the segment OA.
• Build a VO beam
• Measure the length of the segment VO
• Place a segment OB 1 on the ray BO on the other side of point O, equal to the segment OB.
• Connect points A 1 and B 1 with a segment

A 1

IN 1

A 1

WITH 1

IN 1

Centrally symmetrical figures are equal

Construction of a figure centrally symmetrical to a given one

Rotate point A around the center of rotation O by 90 °

A 1

90 °

Rotating points at different angles

A 1

135 °

45 °

A 2

90 °

A 3

Axial symmetry

Shape Transformation F in shape F 1, in which each of its points goes to a point symmetrical with respect to a given line, is called a symmetry transformation with respect to a line A. Straight A called the axis of symmetry.

Constructing a point symmetrical to a given one

2. AO=OA '

Construction of a segment symmetrical to a given one

• AA ’  s, AO=OA ’ .
• ВВ ’  с, ВО ’ =О ’ В ’ .

3. A ’ B ’ – the required segment.

Construction of a triangle symmetrical to a given one

1. AA’  c AO=OA’

2. BB’  c BO’=O’B’

3. СС ’  c С O”=O” С ’

4.  A’B’ C ’ – the desired triangle.

Construction of a figure symmetrical to a given one relative to the axis of symmetry

Figures with one axis of symmetry

Corner

Isosceles

triangle

Isosceles trapezoid

Figures with two axes of symmetry

Rectangle

Rhombus

Figures having more than two axes of symmetry

Square

Equilateral triangle

Circle

Figures that do not have axial symmetry

Free Triangle

Parallelogram

Irregular polygon

“Symmetry is the idea through which man throughout the centuries has tried to comprehend and create order, beauty and perfection.”

If you think for a minute and imagine any object in your mind, then in 99% of cases the figure that comes to mind will be of the correct shape. Only 1% of people, or rather their imagination, will draw an intricate object that looks completely wrong or disproportionate. This is rather an exception to the rule and refers to unconventionally thinking individuals with a special view of things. But returning to the absolute majority, it is worth saying that a significant proportion of correct items still prevails. The article will talk exclusively about them, namely about symmetrical drawing of them.

Drawing the right objects: just a few steps to the finished drawing

Before you start drawing a symmetrical object, you need to select it. In our version it will be a vase, but even if it does not in any way resemble what you decided to depict, do not despair: all the steps are absolutely identical. Follow the sequence and everything will work out:

1. All objects of regular shape have a so-called central axis, which should definitely be highlighted when drawing symmetrically. To do this, you can even use a ruler and draw a straight line down the center of the landscape sheet.
2. Next, look carefully at the item you have chosen and try to transfer its proportions onto a sheet of paper. This is not difficult to do if you mark light strokes on both sides of the line drawn in advance, which will later become the outlines of the object being drawn. In the case of a vase, it is necessary to highlight the neck, bottom and the widest part of the body.
3. Do not forget that symmetrical drawing does not tolerate inaccuracies, so if there are some doubts about the intended strokes, or you are not sure of the correctness of your own eye, double-check the laid down distances with a ruler.
4. The last step is connecting all the lines together.

Symmetrical drawing is available to computer users

Due to the fact that most of the objects around us have the correct proportions, in other words, they are symmetrical, computer application developers have created programs in which you can easily draw absolutely everything. You just need to download them and enjoy the creative process. However, remember, a machine will never be a substitute for a sharpened pencil and a sketchbook.

TRIANGLES.

§ 17. SYMMETRY RELATIVELY TO THE RIGHT STRAIGHT.

1. Figures that are symmetrical to each other.

Let's draw some figure on a sheet of paper with ink, and with a pencil outside it - an arbitrary straight line. Then, without allowing the ink to dry, we bend the sheet of paper along this straight line so that one part of the sheet overlaps the other. This other part of the sheet will thus produce an imprint of this figure.

If you then straighten the sheet of paper again, then there will be two figures on it, which are called symmetrical relative to a given line (Fig. 128).

Two figures are called symmetrical with respect to a certain straight line if, when bending the drawing plane along this straight line, they are aligned.

The straight line with respect to which these figures are symmetrical is called their axis of symmetry.

From the definition of symmetrical figures it follows that all symmetrical figures are equal.

You can obtain symmetrical figures without using bending of the plane, but with the help of geometric construction. Let it be necessary to construct a point C" symmetrical to a given point C relative to straight line AB. Let us drop a perpendicular from point C
CD to straight line AB and as its continuation we will lay down the segment DC" = DC. If we bend the drawing plane along AB, then point C will align with point C": points C and C" are symmetrical (Fig. 129).

Suppose now we need to construct a segment C "D", symmetrical to a given segment CD relative to the straight line AB. Let's construct points C" and D", symmetrical to points C and D. If we bend the drawing plane along AB, then points C and D will coincide, respectively, with points C" and D" (Drawing 130). Therefore, segments CD and C "D" will coincide , they will be symmetrical.

Let us now construct a figure symmetrical to the given polygon ABCDE relative to the given axis of symmetry MN (Fig. 131).

To solve this problem, let’s drop the perpendiculars A A, IN b, WITH With, D d and E e to the axis of symmetry MN. Then, on the extensions of these perpendiculars, we plot the segments
A A" = A A, b B" = B b, With C" = Cs; d D"" =D d And e E" = E e.

The polygon A"B"C"D"E" will be symmetrical to the polygon ABCDE. Indeed, if you bend the drawing along a straight line MN, then the corresponding vertices of both polygons will align, and therefore the polygons themselves will align; this proves that the polygons ABCDE and A" B"C"D"E" are symmetrical about the straight line MN.

2. Figures consisting of symmetrical parts.

Often there are geometric figures that are divided by some straight line into two symmetrical parts. Such figures are called symmetrical.

So, for example, an angle is a symmetrical figure, and the bisector of the angle is its axis of symmetry, since when bent along it, one part of the angle is combined with the other (Fig. 132).

In a circle, the axis of symmetry is its diameter, since when bending along it, one semicircle is combined with another (Fig. 133). The figures in drawings 134, a, b are exactly symmetrical.

Symmetrical figures are often found in nature, construction, and jewelry. The images placed on drawings 135 and 136 are symmetrical.

It should be noted that symmetrical figures can be combined simply by moving along a plane only in some cases. To combine symmetrical shapes, as a rule, you need to rotate one of them reverse side,

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Lessons at school are a significant part of the life of schoolchildren, requiring basic comfort and favorable communication. The effectiveness of the educational process depends not only on the diligence and hard work of students, the presence of targeted motivation of the teacher, but also on the form of lessons.

The use of information technologies allows you to save time when explaining new material, present the material in a visual, accessible form, influence different systems of perception of students, thereby ensuring better assimilation of the material.

Much attention is paid to applying the acquired knowledge in mathematics in everyday life. Acquaintance with beauty in life and art not only educates the child’s mind and feelings, but also contributes to the development of imagination and fantasy. I believe that a lesson with elements of creative activity helps to activate the mental activity of schoolchildren and therefore takes place on a high emotional level, which allows them to consider a large number of theoretical questions and tasks, involve all students in the class in the work. In order to increase student activity, alternation of activities is used throughout the lesson.

At the final stage of the lesson, students complete test work in the form of a test, they conduct a self-test, evaluating their work according to specified criteria. The most active group of students is offered additional material on the topics studied.

Reflection at the end of the lesson helps determine the level of mastery of the material and set goals for further work.

Homework consists of two parts, which allows you not only to continue consolidating the acquired knowledge, but to develop the creative abilities of children.

In my opinion, such lessons give the teacher the opportunity to create, search, work for high results, and form universal skills in students. learning activities– thus preparing them for continued education and for life in constantly changing conditions.

Lesson objectives:

• familiarization with the concept of axial symmetry;
• developing the ability to construct figures that are symmetrical relative to a straight line and to identify axial symmetry as a property of some geometric shapes;
• revealing the connections between mathematics and living nature, art, technology, architecture;
• development of skills to apply theoretical knowledge into practice, development of skills of self-control and mutual control, self-esteem and self-analysis educational activities;
• development of attention, observation, thinking, interest in the subject, mathematical speech, desire for creativity;
• formation of aesthetic perception of the surrounding world, nurturing independence.
• preparing students to study geometry, deepening existing knowledge;

Lesson type: a lesson in “discovering” new knowledge.

Equipment: computer, pin or compass, projector, cards, geometric shapes made of paper.

DURING THE CLASSES

1. Organizational moment

(Slide 1) It’s easy to find examples of beauty, but how difficult it is to explain why they are beautiful. (Plato)

– Today in the lesson we will try to understand some of the features of creating beauty!!!

2. Update

– Look at the maple leaf, snowflake, butterfly. (Slide 2) What unites them, what do they have in common? That they are symmetrical.
– Please remind me what the word “symmetry” means.
– “Symmetry” in Greek means “proportionality, proportionality, sameness in the arrangement of parts.” If you place a mirror along the straight line drawn in each drawing, then the half of the figure reflected on the mirror will complement it to the whole. Therefore, such symmetry is called mirror (axial).

(The teacher shows the experiment on a Christmas tree cut out of colored paper)

– The straight line along which the mirror is placed is called axis of symmetry. If you bend the sheet along this straight line, then these figures fully will coincide and we can see only one figure. What do you think is the topic of today's lesson? (Axial symmetry)

(Slides 3-4)

– Guys, today we will learn how to build figures that are symmetrical relative to a straight line, and you will also learn where axial symmetry is used.
– How can you get symmetrical figures?
– First, let's look at the simplest way to obtain symmetrical figures.
Each of you has a sheet of white paper on the table. Take a piece of paper and bend it in half. Now on one side build a triangle(1st row – acute, 2nd row – rectangular, 3rd row – obtuse).
Further pierce the tops of this figure so that both halves are pierced. Now unfold the sheet and connect the resulting dots-holes using a ruler. Thus, we have constructed figures that are symmetrical to the data relative to a straight line (inflection line). Make sure of this. To do this, fold the sheet along the fold line and look through it into the light.
-What do you see? (The figures coincided.)
– This is the easiest way to build symmetrical figures.
– But in practice, will we always be able to construct symmetrical figures in this way?
– What did we do to build symmetrical triangles?
- Fold the sheet in half.
– That is, draw the axis of symmetry. Further.
– We pierced the vertices of the triangle.
– That is, constructed the points that bound our triangle.
– And this means that before constructing a figure symmetrical to the given one, we must learn to build first what? (A point symmetrical to this one.)
– Let’s figure out how this can be done.

3. Let’s do it now practical work:

– Mark a point Ah. From point A lower the perpendicular JSC directly A. Now draw a perpendicular from point O OA1= AO. Two points A And A1 are called symmetrical about a straight line A. This line is called the axis of symmetry.

(The teacher builds on the board, students in notebooks).

– Which two points are called symmetrical with respect to a straight line?
– How to construct a figure that is symmetrical relative to some straight line?
- Let's try to build a triangle symmetrical relative to a straight line.

(The teacher calls the willing student to the board, the rest work in their notebooks).

After the work done, students draw a conclusion together with the teacher.

Conclusion: To construct a geometric figure symmetrical to a given one with respect to some straight line, you need plot points, symmetrical to significant points ( peaks) of this figure relative to this line and then connect these points with segments.

- Guys, symmetrical can be not only 2 figures, in some figures You can also draw an axis of symmetry. They say that such figures have axial symmetry. Name the figures that have axial symmetry.

(The teacher names and shows geometric shapes cut out of colored paper)

– How many axes of symmetry do you think there are? isosceles triangle, rectangle, square? (A rectangle has 2 axes of symmetry. A square has 4 axes of symmetry) – And at the circle? (A circle has infinitely many axes of symmetry).

(Slides 7-11)

– Name the figures that do not have an axis of symmetry. (Parallelogram, scalene triangle, irregular polygon).

– The principles of symmetry play an important role in physics and mathematics, chemistry and biology, technology and architecture, painting and sculpture, poetry and music. Almost all vehicles, household items (furniture, dishes), and some musical instruments are symmetrical.
– Give examples of objects that have axial symmetry.

– Nature laws, governing the inexhaustible picture of the phenomenon in its diversity, in turn, also obey the principles of symmetry. Careful observation shows that the basis of the beauty of many forms created by nature is symmetry.

(Slides 12-15)

Symmetry is often found in objects created by man.
Symmetry is found already at the origins of human development. Since ancient times, man has used symmetry in architecture. Ancient temples, towers of medieval castles, modern buildings it gives harmony, completeness.

(Slides 18-19)

Symmetry in the visual arts produces impressive results. (Slides 20-21)
Renaissance artists often used the language of symmetry in constructing their compositions. This followed from their logic of understanding the picture as an image of an ideal world order, where reasonable organization and balance reign, which a person can cognize and comprehend.
In an amazing painting "The Betrothal of the Virgin Mary" great Raphael reproduced such an image of the world, existing according to the laws of harmony and strict logic. The principle of symmetry used creates the impression of peace and solemnity and at the same time a certain detachment from the viewer. The entrance to the graceful rotunda and the ring that Joseph puts on Mary’s hand coincide with the central axis of symmetry of the picture.
In progress Leonardo "The Last Supper" Strict construction of interior perspectives prevails. Compositional development here is based on a mirror repetition of the right and left parts. Of course, most often in the visual arts we say about incomplete symmetry.
In the picture "Three heroes" by Russian artist V. Vasnetsov the characters themselves are full of pent-up strength. Because of these small deviations from strict symmetry, there is a feeling of inner freedom of the characters, their readiness to move.
The letters of the Russian language can also be considered from the point of view of symmetry. (Slides 22-23)
The entire alphabet is divided into 4 groups, what criteria do you think I used to do this?
The letters A, M, T, W, P have a vertical axis of symmetry, B, Z, K, S, E, V, E - a horizontal one. And the letters Zh, N, O, F, X each have two axes of symmetry.
Symmetry can also be seen in the words: Cossack, hut. There are entire phrases with this property (if you do not take into account the spaces between words): “Look for a taxi”, “Argentina attracts a Negro”, “An Argentine appreciates a Negro”. Such words are called palindromes . Many poets were fond of them.
Let's look at examples of words that have a horizontal axis of symmetry:
SNOWBALL, BELL, SKATE, NOSE
Words with a vertical axis of symmetry:

X	T
ABOUT	ABOUT
L	P
ABOUT	ABOUT
D	T

Some composers, including the great Bach, wrote musical palindromes.

(Slide 24) Those who are lucky enough to have a symmetrical face have probably already noticed that they are popular with the opposite sex. This may also indicate their good health. The fact is that the face with perfect proportions is a sign that its owner’s body is well prepared to fight infections. Common colds, asthma, and flu are more likely to improve in people whose left side is exactly like their right.

Physical education minute(Slide 25)

Once - rise, stretch,
Two – bend over, straighten up.
Three - three claps of your hands,
Tory nods his head.
Four - arms wider,
Five - wave your arms,
Six - sit down at your desk again.

(Slide 26-27)

A test is carried out followed by self-test.

– Let’s not forget about mental gymnastics. Our examples today are also symmetrical. For those who have already completed the task, you can calculate these symmetrical examples orally. (Slide 30)

Option 1 Option 2

1) B 2) D 3) B 4) A 5) B 1) C 2) B 3) B 4) D 5) D

Evaluating the work performed according to the relevant criteria:

“5” – 5 tasks;
“4” – 4 tasks;
“3” – 3 tasks;
“2” – less than three tasks.

– Try to answer the question which figure is extra and why? (Slide 31)

(Figure No. 3, because it does not have an axis of symmetry)

- Well done!

5. Lesson summary. Reflection

– Our lesson is coming to an end, but our acquaintance with symmetry continues. Throughout the lesson we completed a variety of tasks.
– What concept did you become familiar with today?
– What goals did we set for the lesson? Have we achieved our goals? Who did the best job? Who excelled in class? Which task did you find most difficult? What theoretical material helped you cope with the task?
– Which task did you find most interesting? What new things did you “discover” for yourself in the lesson? What do you think each of you should work on?

- Guys, thank you for your work! Without each other's help and support, we would not be able to achieve our goal. I am very pleased with your work in class. Do you think that we spent these minutes together not in vain? Share your impressions about our lesson.

(Slides 32-33)

7. Conclusion

Truly symmetrical objects surround us literally on all sides; we are dealing with symmetry wherever any order is observed. Symmetry is opposed to chaos, disorder. It turns out that symmetry is balance, orderliness, beauty, perfection.
The whole world can be considered as a manifestation of the unity of symmetry and asymmetry. Symmetry is diverse and omnipresent. She creates beauty and harmony.
And to the question: “Is there a future without symmetry?” we can answer with the words of the classic of modern natural science, the thinker Vladimir Ivanovich Vernadsky, “The principle of symmetry covers more and more new areas...”