Zavantazhiti presentation vіs simmetriії. Axis symmetry. Figuri, which will volodyut one vissyu simmetriya

Axis and central symmetry

“ Symmetry tієyu іdeєyu, for the help of which people stretch out the table re-enhancing and establishing order, beauty and perfection ". nimetsky mathematician G. Weil

symmetry (Meaning "vidpovidnist") - the power of geometric objects to unite with themselves during singing re-creation. From a symmetrical mind, be it correct in the inner budovy tila or figuri.

Symmetry to a point is the central symmetry, and symmetry is very straight - the whole axis of symmetry.

The symmetry of the transfer point, where on the sides of the sides of the point is on the same side, there are some, for example, some points or a geometric combination of points (straight lines, curves of lines, geometric figurines).

The symmetry of the symmetrically straight (axis of symmetry) transmission, along the perpendicular, we draw through the skin point of the axis of symmetry, at the same time there are two symmetrical points. Simultaneously, the axis of symmetry (straight) can grow as well as geometric shapes, which are known to the point of symmetry.

The length of the symmetry serves as a perpendicular to the middle of the horizontal lines to flank the sheet straight. Symmetric points (R і F, C і D) are rotated on the same side from the axial straight line - perpendicular to the straight lines from the bottom point. Otzhe, all specks of the perpendicular (axis of symmetry), drawn through the middle of the winding, straight forward from the end; For be it a point of perpendicular (axis of symmetry) to the middle of the direction of the distance is from the end of the line.

If there is a straight symmetrical point (points of a geometric figure) through the point of symmetry, then the symmetrical points lie on the straight lines, and the point of symmetry will be the middle. If you close the point of symmetry and wrap it straight, then the symmetrical points describe the curves, the skin point of which may also be symmetrical to the point of the curve line.

Symmetry in architecture

For a long time, Lyudina vikoristov has been simulating symmetry in architecture. The symmetry in the architectural traditions of ancient architects was especially blisky. Moreover, the old Greek architects have been overcontained, in their creations they stink with laws, like nature. Vibrating symmetrical forms, the artist himself was able to catch his own mind of natural harmony as a style and a rhythm. Temples dedicated to the gods, and are guilty like this: the gods are everlasting, they do not care for human turbos. Most clear and timely awakening from a symmetrical composition. Old temples, basht of middle-aged castles, fortunate fortunes simmetry nadaє harmony, finality.

Sphinx in Gizi

Aswan Mosque in Egypt

Symmetry in mystery

Symmetry is victorious in such types of art as literature, Russian language, music, ballet, jewelery art.

Yaksho pride itself on the handled letters M, P, T, W, V, E, Z, K, S, E, F, H, O, F, X, you can pachiti, the stench is symmetrical. Moreover, in the first ones, the symmetry runs vertically, and in the first six - horizontally, and the letters Zh, N, O, F, X may run along two axes of the symmetry.

ornament

Ornament (from Latin ornamentum - embellishment) is a vіzerunok, which can be formed from repeated, rhythmically ordered elements. Vin can be striking (they call it a border), often and rosette. Ornament inscribing in colo abo in correct bagatokutnik, Call yourself an outlet. The common ornament will keep the entire surface of the surface with a suction vise. The border should be moved in parallel with the transfer of the straight line.

mirror symmetry

The symmetry of the square in deyakie dzherels is called mirror-like. With the attachments of post-article-mirror images, one by one, we can serve the rights and the hands of the people, the right and the hands of the people, the right and the left gvinti, part of the architectural forms.

Lyudina is instinctively pragmatic to style, lightness, beauty. Tom is drawn to objects, which have more symmetries. Why is symmetry acceptable to the eyes? Mabut to the fact that there is a symmetry of panun in nature. From the people of Lyudin to bilaterally symmetrical people, comas, birds, ribs, tvarin.

heavenly symmetry

A world of snow crystals are falling to the ground. Oh, I am cold to perfection and absolute symmetry of the enemy. To navigate old enough for an hour, the fall is drowned, as in the childishness, the individuals go to the sky, to catch the great babies and to be fascinated by the eyes, they landed on the valley of the crystal. і "cooler", simply or folding "zіrochki" with strongly rounded flaps - they are still called dendrites.
Glaciologists - vchenі, yakі vivchayut forms, warehouse і Budova ice, store, scho leather sіgovy crystal is unique. However, all the girls may be healthy rice- the stench may smell hexagonal symmetry. In addition, the "little stars" will have three, six or twelve changes. Nayridkisnisha twelve-pointed "little star" pops up in thunderous gloom.
The first systematic preliminaries of the cynical crystals were made in the 1930s by the Japanese physicist Ukikhiro Nakaya. Win vidiliv 41 types of snacks and sklava pershu classification. In addition, when I try to make the first "piece" slick and z'yasuvav, the size and shape of the crystal in the ice will be deposited at the temperature of the second and the second.

palindromy

Symmetry can be poured in all words, such as "Kozak", "kurin" - the stench is read the same way as evil to the right, so from right to left. And the axis of the whole phrase is with such a power (as if it is not vrahovuvati glaze away with words): "Shukati dachshunds",

"Argentina Man'am Negro",

"Tsinuh Negro Argentinian",

"Llosha on the police the bedbugs know",

"And in Onisei - blue",

"Misto Dorig",

"Do not nod."

Such phrases and words are called palindromes.

Malinki, viconani by scholars

Symmetry is one of the most fundamental and one of the most remote laws of light: inanimate, animate nature and suspension. With the symmetry of my vision everywhere. The understanding of the symmetry goes through the entire history of human creativity. Look out for the same rounds of human knowledge; yogo broadly vikoristovuyt all without a blame straightforward science.

Symmetry of the presence of the day: in the regularity of the day and night, feast, in the rhythmic inducement of the wind, it is practical there, as the presence seems to be in order and regularity.

There is a senseless kind of symmetry in both the rose and the food light, albeit with all the development of living organisms, the principle of symmetry is the principle, and the fact is, once again, the natural harmony of ours.

Kerivnik Zhadanova Zoya Vasilivna MBOU ZOSH № 3 m Voronezh

symmetry
axis symmetry
zavdannya
Symmetry in geometry, nature, architecture, travel

value

Symmetry (from the Greek. Symmetria - appearance), in a wide sense - the inviolability of the structure of the material object and its transformation. Symmetry of the city is a majestic role in art and architecture. Ale її can be remembered both in music, and in travel. Symmetry is widely developed in nature, especially in crystals, in roses and animals. Symmetry can be implemented in some of the branches of mathematics, for example, when prompting graphs of functions.

axis symmetry
Two points, which lie on one perpendicular to a given straight along the sides and on the same side, are called symmetrical, as a matter of fact.

Figura is called symmetric, apparently straight a For the skin point of the figuri, it is symmetrical; the point is fairly straight a so it is possible to lay out the tsіy figurі.

Figuri, who will volodyut one vissyu simmetriya

kut

pivnobedreniy

trikotnik

pivot trapeze

Figuri, scho volodyut two axes of symmetry

rectangular

rhombus

Figuri, which may be more than two axes of symmetry

square

Equilateral trikutnik

Figuri, do not volodya axial symmetry

parallelogram

good tricycle

pobudova
points symmetric to the given
symmetric to the given

Pobudova point, symmetrical given
1. AOs
2. AT = OA '

Pobudova vidrizka symmetrical to the given
1AA's, AT = OA '.
2ВВ's, BO '= О'В'.
3. A'B '- shukaniy vіdrizok.

Show point A ', but lie in the first quarter

coordinate area.

Point A is symmetrical to point A 'along the y axis.

Point C is symmetric to point A along the x axis.

Point D is symmetrical to point C with the axis of y.

You can say:

about points A and D

about figuru A ' ACD

for me, wash A 'A CD will be square

as follows:
Points A and D are symmetrical to the axes.
ABCD - rectangular
From point A to axis x and y to be equal

... Granting to the Neva;
Bridges hung over the waters;
dark green gardens
Її the islands crept ...

Pushkin A.S. "Midniy verhnik"

The theme "Axis symmetry"

Oleynikova Galina Mikhailivna,

Municipal government treasury mortgage "Yablochenskaya middle zagalnoosvitnya school»

Khokholsky municipal district Voronez region

"Mathematics is in order, symmetry and value, and the whole thing is beautiful."

Aristotle (384 - 322 BC)

technology problematic navchannya

Subject "Mathematics"

Meta lesson: organizing the productive activity of scientists, directing them to reach such results:

metasubject results:

v educational performance:

help scholars learn social, practical and special significance of new material;

vicoristovuvati for learning about new methods of new methods (caution, vimiryuvannya, dosvid, experiment, modeling, etc.)

ordering, placing, classifying objects and objects one at a time, or a decal of proponent criteria;

self-determination of creative creative work;

participation in project activities;

in information - Communicative activity:

of writing their lingering, adequately transmit the listened and readinformation with a given level of flare-up (short, vibrating, again)

given notepiv, pidbir arguments, formulas for visnovs;

visualization in usn_yand writing forms of results in their activity;

at the tendency to rephrase the thought (explain it with "in words");

victorian for the reception of educational and communal establishmentsnew dzherel information, including encyclopedia, wordsri, Internet resources and іnshі bases danih;

in reflexive activity:

appraisal of their chiefs dossignen;

assimilation of the valuespheres of their interests and possibilities;

volodinnya vminnyi spіlnogo dіyalnosti: uzgodzhennya and coordination performances with other participants; actively assess svogo annotation at the show of the zagalny employees to the team;

assessment of one's own performance from the point of view of moralnorms and natural values;

hittrimannya rules a healthy way of life.

special results:

Introduced and easily displayed geometric inspiration;

take in your thoughts in letters;

speak good and easily catch your thoughts;

formvati character;

you will be able to find out how to fix the knowledge and tips until new problems are resolved;

mirkuvati is logical;

vmіt fіksuvati vlasnі difficult, wіll see thе reason, buuvati wіth wіkhodu sі twist;

subject results :

vmіti buuvati points, figuri, symmetrical data;

direct the butt of symmetrical objects in the field of action;

to spend an additional time with those given in nature and architecture;

Mastering the ways of doing things, which can be learned at the lesson of mathematics from integrating into anatomy, biology, ecology, culture of a healthy way of living, architecture.

Lesson type: lesson-doslіdzhennya.

Form robots: individual, paired, group, frontal.

ustatkuvannya: Computer cabinet with access to the Internet, projector, screen, presentation, figurines-tokens, little ones, magnets, color credit; the leather schoolboy has a folder with a set of geometric models, school tools, color papir, color olives, knives.

methods: Explanatory-illustrative, part-sound, pre-slidnitsky, project.

Forms of educational activity: Frontal, individual.

Before learning from the first lesson, those "Axis symmetry" are grouped (for bazhannya and interests) into 3 groups, equal to the number, such a rank, that the skin group bully scholars, as they may be in the house of others. The skin group will reject the zavdannya for mini-dosljennya: symmetry in nature, anatomy of people and architecture.

After an hour of the lesson, the group is saved. For the skin correctly, the team will remove the figurine-token. One figurine, one ball. The team, which scored the most points, will take the rating 5; two people carry out self-assessment in the middle of the group.

Actualization.

We are alive in a smart - small, high-tech, informational support, and not mind that the objects and things that are in our minds awaken a sense of beauty, but the things that are beautiful.

vlіtku - Bozha korivka... basic chew the leaves on trees or leaves, fell to the ground - even more beautiful. And what about the charge? - Snowflakes.

Mi ydemo on the streets and raptom moving croc, shaking proportionally and beautifully.

Let me pass through helpless people, and I have a lot of respect for someone else, and say: "Tsya lyudina is garnishing and harmonious."

Tsey lantsyuzhok can be prodovzhuvati, ale at once we say forgiveness to one: about beauty, harmony and proportionality of living and inanimate nature.

I ask (I ask you to go specially prepared) for a student. Children zvratayut respect for symmetrical stripes, earrings, blouse, shawl with symmetrical baby.

Today our classmate is our guest and she calls herself ...

- "Simetria".

For the first time, we will touch you with a wonderful mathematical phenomenon - the axial symmetry. (Slide 1-3)

It is possible to write down the topic for the lesson "Axis symmetry".

During the season, we will try to adapt to the next meal:

What kind of symmetry?

What is the axis of symmetry?

Immediately on the start of symmetrical figurines.

It is repeated to induce symmetric points and geometric shapes in an apparently straight line.

Yaku role vіdіgraє symmetry in haunted life people (in nature, architecture, in the house)?
- Why is it possible, I know about the tame harmony, we grow light and beautiful?

The teacher and the learner write down the number, the class of the robot, the topic of the lesson in school and zoshiti.

Let the proponate to the scholars the vibrations from the proponents of the special purpose (or the special results) on the screen; Scientifically viznachayut for themselves special results (vibrating from the list on the screen), until which will be pragmatic at the level, and the number of the order (in the fields) in the zoshiti.

Frontal besіda.

What kind of symmetry? (Slide 4-8)

The word simetrya has long lived in the meaning of harmony and beauty.

The comprehension of Evklid, Pyfagor, Leonardo da Vinchi, Kepler and the most misleading people of the people were magical about the harmony of the harmony.

“Symmetry is the idea, behind the help of some people, they will explain and set up the order, beauty, perfection” G. Weil.

Can you tell me about the meaning of the word "symmetry" and "hang"?

Symmetry is the same thing, the appearance in the spreading of parts of something on the opposite sides of a point, straight or square.

The axis is straight (there is a clear line to pass through the geometric figure, which is only the power of the authorities).

Are these points called symmetric?

The value of symmetric points is relatively straight:

"Two points A and B are called symmetric, apparently straight p, as it is straight to pass through the middle of the curve AB, but from the same point and perpendicular to the new one."

Formulate an algorithm to induce a point symmetric to a given straight line.

Why can't you be viconati zavdannya, yak sound offensive rank: "Induce a figuru, symmetrical tribute"?

Tse zavdannya not so much, to that it is not clear, when to vikonuyutsya symmetry: but a point is abo vidno straight. This means that for the vison of the axial symmetry, the nobility of the symmetry is necessary.

Closing the material.

1) .Construction of figurines, symmetrical given (estafet by groups)

The letters of the robot in zoshits and in letters. (Slide 9-12)

zavdannya 1. Induce a point that is symmetrical to a tribute to an admittedly straight line a.

Zavdannya 2. Indulge in a direct, symmetrical tribute to an admittedly direct m.

Zavdannya 3. Induce a trikutnik, symmetrical to the given, admittedly straight.

Zavdannya 4. Paint from the hands of the figuru, Symmetrical tribute to the vertical axis (yalinka, bird, cat). (Slide 13)

Figuri namalovanі on arkusha and fastened to the board. Leather walks to the door and to rob one element of the image, symmetrically one figure from the quiet, so proponated by the command. The team wins, like the Persha to fit into the team. Assessment is carried out according to the offensive criteria:

Encourage the correct vison;

Aesthetic beauty;

Participation of the cutaneous member of the group.

zavdannya 5 (sleep robot ). Chi vіrno, scho such numerical prominence simm Straight line m, perpendicular to the coordinate line and go through the cob. Pro:

a) from 3 to 7 and from -7 to -3;

b) from 10 to 25 and from -25 to -10;

c) the environment of the interchange from 1 to non-termination and from the minimum to 1?

View: a) so; b) dumb; c) so.

Zavdannya 6. Doslidnitska robot"Know the axes of the symmetry of geometric figurines."

Yak visnachiti chi maє figura axis of symmetry? (Slide 14-18)

Bend її.

So, efficiently, as long as the images are cut off, then the right of the part to fall. Such figuri are symmetrical, apparently straight, and the cya is straight - vissu symmetry.

And the symmetry axes can be the mother of a figure? On the desks you have geometric shapes. Your zavdannya self-reliance, skіlki axes of symmetry may be skin figure. Look for the "symmetrical" and "asymmetric" figurine itself.

You can start to know the axis of symmetry of such geometrical figures yak kut, equilateral, tricycle, rectangular, rhombus, square, trapezium, parallelogram, colo, irregular bugger.

Z'yasuєmo, like geometric figures, can you imagine one symmetry?

kut, tricytnyk wedge, Trapezia.

Two axes of symmetry?

Rectangle, rhombus.

I am the chi diagonals of the rectangle with the axes of symmetry, and for what?

Chi not є, so when bending the rectangle along the diagonal, the tricycles do not bend.

Scientists cross the figure along the diagonal and show that the parts of the rectangle do not get lost, so that the diagonal of the rectangle is not all symmetrical.

Three axes of symmetry?

Equilateral trikutnik.

Chotiri axis of symmetry?

Square.

Are the symmetry axes small?

Unlich. Tse straight, go through the center of the stake.

Otzhe, yaka Is the figure itself “symmetrical” and is it itself “asymmetrical”?

Itself "symmetric" - about, and "asymmetric" - versatile trikutnik, parallelogram; bagatokutnik, which side is not equal.

Zavdannya 7 ( sleepy) ... Place the symmetrical objects in your surroundings around the booth and on the street? And my friend with you will be symmetric?

Zavdannya 8 (Doslidnitska and "kraєznavcha" robot-10 points).

I propose to spend a mini-session in pairs or small groups with further discussions about the manifestation of symmetry in the inner and outer Budov of people, tvarins, roslinas; in architecture for the future of the country, our place and school.

When you are ready, you will start to browse the Internet.

Results mini-doslijen represent the academic class. The Skin Group of Scientists presents the results and reports on the following topics:

Axis symmetry and nature.

Axis symmetry and lyudin.

Axis symmetry in architecture.

Create a powerful product in a written presentation and presentation.

Zakhist be assessed by:

Optimally assigned material,

Laconic wiklade, logical mirkuvan,

Aesthetic beauty,

Stuck in the life of the people.

- "Axis symmetry in nature ".(Slide 19-22)

I will show more carefully how the basis of the beauty of the forms created by nature becomes symmetry. Yaskravoy twisted symmetrical leaf, quit, fruit.

Doslіdzhennya ecologists tightly tied with dewy weeds and trees.

For the symmetry of the birch leaf, we can talk about the healthy ecological situation in the microdistrict. As the birch leaves are not symmetrical, the ecological situation is unfriendly, and it is prone to the appearance of radioactivity or chemistry. Doslidzhuєmo birch leaves, picked up in the microdistrict of the western Bataysk. On the basis of distribution material robimo visnovok, which is ecologically friendly to the microdistrict.

Wine siple from the sky with dry cereals, lithuanians near lichtars with magnificent fluffy plastics, worth one hundred percent in a thousandth of a light with crooked heads. Hello b, yak nіsenіtnytsya! Only the water froze. ... ale skіlki food vinnikє at the people, you can marvel at the snіzhinki.

snіzhinka - a whole group of crystals, approved by more than two hundred kryzhany particles.

symmetry - the value of the power of the crystals will be one by one in different positions by way of turns, parallel transfers, views.

Practice the axis of symmetry in your model of a girl.

- "Axis symmetry and creative light". (Slide 23)

If you start to see the symmetry of the new budov and the twarin, put your butt on the symmetrical color, and just start talking about those who internal budov creatures are not symmetrical.

- "Axis symmetry and lyudin". (Slide 24-25)

The beauty of the human body is enveloped in proportion and symmetry. Internal organs of Budova are not symmetrical.However, the human figure can be asymmetric. One of such butts is scoliosis - a ridge vikrivennya, podbane, including the wrong position.

Scoliosis - lateral distribution of the ridge - more often than not, at times from 5 to 16 rocks. Approximately 5-10% of children suffer from 5-10% of children with scoliosis, until the end of school and scoliosis appears in more than half of children.

One of the main reasons is the wrong posture before hour to occupy, Through the yaku, the winery is nerivnomirne navantazhennya to the ridge і m'yazi. What kind of insecure scoliosis and what kind of ailments can be brought to the public?

Most of the organs of the human body can be easily controlled from spinal cord through the spinal nerves. The imprint of the cores of the nerves, which enter the spinal cord, leads to the destruction of the robotic internal organs. Hippocrates introduced the connection between the ridge and the functions of the internal organs. Prevention of scoliasis is more beautiful, lower thirst.

When pershit Find our skolіozu neobhіdno prokonsultuvatisya of fahіvtsem, vikonuvati mode yaky polegshuє navantazhennya the ridge, zabezpechiti Bhagat vіtamіnami i mіneralnimi rechovinami harchuvannya (ridge Wkra neobhіdnі takі mіkroelementi kaltsіy yak, zinc, mіd) potrіbno zaymatisya rankovoyu gіmnastikoyu i lіkuvalnoyu fіzkulturoyu. It is important to get right to sit at the writing table: it’s because of the three incursions and the three backs, and the three of the omissions. With this position of the head, the entire ridge is straightened and blood flow to the brain is increased. Legs are guilty of standing on pidlosis, moreover, the kut in knee slopes is guilty of folding approximately 90 degrees.

The ridge is one of the most important storage parts of the human body. Zavdyaki youmu mi can go, bigati, stribati, come. Look, put a lot of beauty and charm of people.

80% of Russian children suffer from different types of deterioration of posture from flat feet to scoliosis. The formation of the viginous ridge will end in 6-7 years and close up to 14-17 years. And it means that in the whole period of the day it is important to put it right and lay the foundation of health on the way forward.

The destructed place is not sickness, but the camp, like a pidlyagaє korektsii. It seems that up to 21 rock, as long as the organism grows, it is possible to get sick of the cyst-myase system. I teach all the participants of our lesson the quilts for the correct setting.

- "Axis symmetry in architecture of the city of the world, of the city of Bataysk."(Slide 26-32)

All the symmetry is visible in architecture. At the age of old Greek architects, symmetry has become a separate regularity, professionalism, beauty. With the help of such sporu there are the Pyramid of Cheops in Egypt, the Cathedral of Our Lady of Paris and the Eiffel Vezha in France, Big Ben in Great Britain, the Taj Mahal mosque in Turechchina.

The architecture of the Russian Orthodox churches and cathedrals to inform about those who found the clock in the architecturethey knew well the mathematical proportion and symmetry and they were victorious when they were awake architectural projects Rusi: Kremlin, Cathedral of Christ the Savior Moscow, Kazan and St. Isaac's Cathedral in St. Petersburg, Cathedral in Pskov, Nizhny Novgorod and іnshі.

We asked one more nourishment: "Is the current architecture the secret of beauty?" Of interest to us is a native place. For example, the symbol of Bataysk, which is located in the Central Park, fell in love with the city dwellers, aesthetically speaking, it can be explained by the symmetry of the arch. Mi bachimo symmetry in administrative, living quarters, cultural events.

The name of the Holy Trinity Church is the main memorial of the place, by the architectural canons to inspire Russian cathedrals, by the addition of symmetry and proportion. Vivchayuchi memorial "Oath beckoning" and memorials we z'yasuvali, how the stench was taken on simmetriya. Budіvlya zalіznichny railway station of our place is also a kind of symmetrical waking up. In such a rank, there are a lot of buddies, which form the guise of our place of harmony and adhere to the laws of beauty.

- "Axis symmetry and our school yard". (Slide 33)

Prior to the development of the native schools of bachimo, the facade of the building, the ganoks, the section of the school fence, the small architectural forms, the flowerbeds adhere to the rules of symmetry. Tom zagalny viglyad shkіlnogo courtyard viglyadaє harmoniously.

Reflexion. (Slide 34-37)

- The slides of the presentation show the butt of symmetrical and non-symmetrical objects in the light of the day (3 slides). Scientists learn how to understand symmetrical and asymmetrical objects, to analyze what?

Home zavdannya:

- creative work on the theme "Vyslovlyuvannya great vchenykh about symmetry";

- mini-presentations, photo reports about symmetry of new actions;

- open models color papir, Knives, felt-tip pens;

itscreativity zavdannya.

visnovka... (Slide 38)

Axis symmetry is a mathematical understanding.

Symmetrical figurines started to appear.

There will be a number of symmetrical points and geometric shapes that are always straight.

Symmetry-tse harmony.

The tantalum of harmony was enchanted by the comprehension of the great misters of the people. Years at the lesson in the puzzle of the tsієї tamnitsі zanurilis and mi. Z'yasuvali, where the symmetry of the face is one of the head straight in the haunted life of the people: in objects, in architecture, in nature.Knowing about the mysterious harmony, one of which is the axis of symmetry, you can grow light and beautiful.

Know the phrase: "Beauty vryatuє svit?" Vazhko not wait with Fedor Mikhailovich Dostoevsky. We all want to grow our life harmoniously and beautifully. Hello, yak you think, can we know the secret of beauty?

Pids bags for the lesson.

What kind of a problem was given to the lesson, what new knowledge did you get at the lesson, what did you get, how difficult and allowed the stench to go?

Ratings are published in the journal and scholars of scholars. The team scored the greatest number of points in the scientific groups with the highest special results and received a rating of 5; the team took another mice-assessment 4.

The designation of Symmetria (in Greek. Symmetria - appearance), in a broad sense - the inviolability of the structure of the material object is often reworked. Symmetry of the city is a majestic role in art and architecture. Ale її can be remembered both in music, and in travel. Symmetry is widely developed in nature, especially in crystals, in roses and animals. Symmetry can be implemented in some of the branches of mathematics, for example, when prompting graphs of functions.

Pobudova vidrizka, symmetric to the given A c A B B O O "1.AAc, AT = OA. 2.BBc, BO = OV. 3. AB - shukaniy vidrizok.

1. Vidrizok AB, perpendicular to the straight line s, overflowing at point O so, scho AOOV. Are the symmetrical points A and B relatively straightforward? 2. Straight and rewind from the MK in the middle of the cut, from the straight line. Symmetrical points M and K are relatively straight? 3. Points A and B roztasvani in small areas with a cordon p so that there is a perpendicular straight line AB and extends along it. Symmetric points A and B are relatively straight p? zavdannya

4. What are the coordinate axes of the symmetrical point M (7; 2) and K (-7; 2)? 5. Points A (5; ...) and B (...; 2) are symmetrical to the axis Ox. Record missing coordinates. 6. Point A (-2; 3), B is symmetric; point C is symmetric to point B in relation to axis Oy. Know the coordinates of the point C. 7. Point A (3; 1), B is a symmetric point with a relatively straight line y = x. Know the coordinates of the point V. Zavdannya

8. For skin problems, presenting on a baby, induce points A and B, symmetrical to points A and B, straight lines. U A z A B z AB z Perevir yourself

8. For skin problems, presenting on a baby, induce points A and B, symmetrical to points A and B, apparently straight with. В В В В АА А А В А А А А А В В В В В В А А А А А В В

Visnovok Simetria can be seen everywhere, as nobility, as shukati. There are a lot of people from the founding hours volodya or to the statements about symmetry in a wide sense - like about the timing and harmony. Creativity of people in all its manifestations is heavy to symmetry. Behind the help of the symmetry of the people, I became aware, behind the words of the Nimetsian mathematician Hermann Weil, “to understand and establish order, beauty and perfection”.

Zmist Central Symmetry Central Symmetry Central Symmetry Central Symmetry Vdannya Tasks Pobudov Pobudov Pobudov Central Symmetry in the New World Central Symmetry in the Central Symmetry in the Central Symmetry in the Central Symmetry

Zavdannya 1. Vidrizok AB, perpendicular to the straight line from, overflowing at point O so, scho AOOV. Symmetric points A and B relative to point O? 2. Chi may be the center of symmetry: a) vidrizok; b) promin; c) a pair of cross-hairs; d) square? A B C Pro 3. Indulge the kut, symmetrical kutk ABC to the center of O. Perevir yourself

5. For skin problems, presenting on a small one, induce points A 1 and B 1, symmetrical points A and B to points O. B A A B AB Pro Pro Pro Pro Z MR b at the central symmetry with the center O. Perevir yourself Dopomoga

7. Induce a good tricycle and thigh image of the point of overturning of thighs. 8. Driving AB and A 1 B 1 centrally symmetrical to the center of C. Encourage the image of the point M at the same symmetry for an additional one line. А В А1А1 В1В1 М 9. To know on the straight lines a and b points, symmetrically one to one. a b O Perevir yourself Supplement