Trikutniki are equal to three sides. The third sign of equanimity in trikutniks. More lessons - Knowledge Hypermarket. Zavdannya to encourage trikutnikiv

Signs of equanimity of tricycles

Rivnim is the name of tricycle, in some of the sides of the line.

Theorem
Yakshho two sides and kut, laying between them, one tricycle, one way to two sides and kut, we put it between them, one tricyt, then such tricytniks.

Theorem (another sign of the equanimity of trikutniks).
If the side and two knots of one tricycle are attached to it, we will rest on both sides of the tricycle, then both tricycles are of the same size.

Theorem (the third sign of the equanimity of trikutniks).
If the three sides of one tricycle are identical to the three sides of the other tricycle, then such tricycles are equal.

Signs of tricycles

Some are called tricycles, some kuti are equal, and some are proportional to the side :, , De - kofіtsієnt podіbnostі.

I signs of tricycle tricycles. Whenever there are two kuti of one tricycle, the two tricycles are similar to each other, then the tricycles are similar.

II signs of tricycles. Just as three sides of one tricycle are proportional to the three sides of another tricycle, then those tricyttes are similar.

III signs of tricycles. As the two sides of one tricycle are proportional to the two sides of the other tricycle, and the kuti, laid between the two sides, are equal, then these tricytes are similar.

In the distant hours and donin poshuk signified the eagerness of figures to get involved in basic enterprises, as є the basis of the foundations of geometry; Hundreds of theorems are brought to the test as a sign of equanimity. Cleverness to bring the balance and flexibility of figures is more important in all spheres of life.

In contact with

Freezing of tips on practice

Admittedly, we have a figura, leaning on the archway of the paper. At the same time, we have a line and protractor, for the help of which we can freeze dozens of forms and cutters among them. Yak to transfer to another arkush the paper of a figur of the same size or the scale of two times.

We know that a tricycle is a tse figure, which is made up of three ways, which are called parties, make kuti. In such a rank, there is a set of parameters - three sides and three kuti, which start a figuru.

However, having frozen the size of all three sides and kutiv, transferring the figure to the top of the surface will appear to the difficult employees. Besides, sense to supply power: but there is little knowledge of the parameters of two sides and one cut, for all there are three sides.

Having frozen the two sides and between them, then put the cut on a new sheet of paper, so I can add the tricycle. Let's get rid of, as the goal of the development, which can bring the signs, for which it is possible to use the same, and for that, as the minimum number of parameters to reach the nobility, to remove the memory from that, however, the tricytes

Important! Figuri are called the same, as they are like, they make their side, and they cut their sides. Let's call them figuri, on both sides and kuti proportions. In such a rank, parity is the price of choice with the ratio of proportionality 1.

There are signs of equanimity in tricycles, ladies and gentlemen:

Persha is a sign of equanimity: two trikutniks can be put in the same way, as well as on two sides, as well as kut between them.
another sign of equanimity of tricycles: two tricycles will be the same, as well as two tricycles, as well as the side between them.
the third sign of equanimity of tricycles : Trikutniki can be respected as the same, if all the parties are ready to eat.

Yak to bring, scho trikutniki pivnі. Hopefully proved the merits of tricycles.

Proof 1 signs

The most recent hour of the middle mathematicians was given a sign of being involved in an axiom, protest, as it appeared, it can be geometrically brought, spiraling on a larger base axiomi.

Two tricycles are visible - KMN і K 1 M 1 N 1. The side of the KM can also be used for the same yak і K 1 M 1, and KN = K 1 N 1. But the MKN cut-out is for the KMN і M 1 K 1 N 1.

If you look at KM і K 1 M 1, KN і K 1 N 1 as there are two interchanges, which go from one point, then it is possible to say that there are two exchanges of the same kuti (the price is given by the theorem). A very parallel transfer of the exchange K 1 M 1 and K 1 N 1 from point K 1 to point K. During the previous transfer of the exchange K 1 M 1 and K 1 N 1 to the back. It is shown on the K 1 M 1 walkway until the KM is finished, so that the ear is kept at the point of K. Similarly, with KN and K 1 N 1. In this way, carrying K 1 M 1 N 1 so that the points K 1 and K are added, and the two sides are applied, it is possible to remove the additional zbig and the figures themselves.

Important! In the Internet, it is possible to prove the equanimity of tricycles behind two sides and a cube for additional algebraic and trigonometric convergences with the numerical values of sides and cuts. However, historically and mathematically, the Boolean theorem was formulated back to algebra and earlier, below trigonometry. For proving the signs of the theorems, vikoristovuvati is not correct, except for the basic axioms, it is incorrect.

Proof 2 signs

A friend of the sign of ryvnosti is brought along two kutas and sides, primed on the first.

Proof 2 signs

Clearly KMN and PRS. To the door P, N to the door S. The KN side can also be used, yak and PS. It is necessary to inform that KMN and PRS are the same.

The point M is imaginable when changing KN. Otrimanu point called L. When tsomu dozhina side KM = KL. NKL door PRS. KNL door RSP.

Oskilki sum of kutiv to 180 degrees, then KLN to PRS, and to mean PRS and KLN - the same (similar) by offense to sides and roses, it is worth knowing.

Ale, so as KNL is road KMN, then KMN and PRS are two of the same figuri.

Proof 3 signs

Yak stand up, scho trikutniki pivnі. Tse is straightforward to prove other signs.

Dovzhina KN = PS. Oskilki K = P, N = S, KL = KM, if KN = KS, MN = ML, then:

Tse means, how offended figuri є take one to one. Ale is so yak on the side of the same, then the stench is equal.

It is a sign of the vigor and the need for viplivation without any problems. One of them is in the fact that, in order to be more important, it is necessary for the nobility of their power, however:

all three sides;
offended parties and kut between them;
offense kuta and the side between them.

Vikoristannya signs of equanimity of trikutniks for the revision of the plant

Traces of the first sign

In the course of the proof, you can come to a number of tsikavi and korishnye heritage.

... The fact that the point of overturning the diagonals of the parallelogram is to extend them into two parts of the same - inheritance is a sign of equanimity and a complete proof.
Yaksho є two rectangular tricycles, which are of the same quality, the stench is subtle. If you have the first leg of the first leg of the other, then the stench rіvnі. It is easy to reach the intelligence - if you have rectangular tricyclesє straight kut. That is a sign of equanimity for them more simplicity.
Two tricot shoes with straight kutas, for which two legs may have the same dyno, you can use the same ones. It is tied together with two legs, which are tied up to 90 degrees. To the one behind the first acquaintance (on the two sides and the cuffs between them), all the tricycles with straight cuts and the same legs - rivnі.
Yaksho є two rectangular tricycles, and they have one leg and hypotenuse, which means they are the same.

Let us prove a simple theorem.

Є two rectangular knitwear. One side a, b, c, de c - hypotenuse; a, b - legs. The other side has n, m, l, de l - hypotenuse; m, n - legs.

According to the theorem of Pyphagoras, one of the catheters of the door:

;

In such a rank, if n = a, l = s (the parity of the legs and the hypotenuses), apparently and other legs will be equal. Figuri, apparently, will be behind the third acquaintance (behind the three sides).

Significantly one more important heritage. Yaksho є two tricycles, and the stench is similar with a certain number of factors, so that there are two pairs of all sides of the road, then the space is placed on the road.

The first sign of equanimity of trikutniks. Geometry video tutorial 7th grade

Geometry 7 First sign of equanimity of trikutniks

visnovok

We have looked at the topic to help anyone learn more beautifully in the basic geometric concepts and advise their own tips in to find mathematics.

Pidgorny Maxim

material pre-slidnitsky robots you can vikoristovuvatisya for the group of geometries in the 7th grade

Zavantazhiti:

Front view:

MBU DO Mіsta Rostov-on-Don "Palace of creativity for children and youth"

Don Academy of Sciences for Young Presenters. Yu.A. Zhdanova

Maths

Topic: "Non-standard theorems about the equality of tricycles"

Pidgorny Maxim, grade 7,

MBOU ZOSH No. 3,

kerivnik:

Oleynikova Lyudmila Oleksandrivna,

mathematic teacher,

MBOU ZOSH No. 3,

m Salsk, Rostov region

m Rostov-on-Don

2017 rik

Introduction ................................................. .................. .................. 3

Main part

Signs of equanimity of tricycles ............................................... .... 4

Non-standard signs of equanimity of tricycles ............................... 7

Visnovok ................................................. ............................. ten

List of Literature ................................................ ..................... eleven

supplement

Entry.

relevance:

Trikutnik is one of the main figures in the planimetry. I am a lot of chuv іd high school students, so when preparing to ІДІ їм it is often brought to the parity of tricycles. I see a lack of knowledge of the main signs. I wanted to know, but I can bring the parity of tricycles for the same parameters. At the handler of geometries, for those who are looking for scientists of our school (author L.S.Atanasyan, V.F.Butuzov and in. Geometry 7-9), there are only 3 signs of equanimity of tricycles. I glanced over at the initial-methodical sets of the authors. And in them only three kinds of theorems are proposed for vivchennya.

hypothesis:

You can, how can you articulate, except for three people, what are the signs of the merits of tricky people?

I’m sure that I’m not only getting better at the food chain, I’ve provided social science for the average of 7-11 classes of divas. Dodatok 1).

My pripuschennya was confirmed. Most scholars know only three signs of equanimity of tricusters.

Such a rank, marked by my presentiment, was the discovery of new signs of equanimity of trikutniks.

zavdannya:

To study the literature from the previous ones.

ΘSpecify the number of signs of equanimity of tricycles.

ΘDemonstrate to your classmates and pupils of our school and to show them the signs of the merits of tricycles and the ability to prove them.

Ob'kt doslіdzhennya:

Vivchennya is a sign of eagerness for trikutniks.

Subject Doslіdzhennya... Trikutnik, yak one of the main figures in the planimeter.

Continuing method:Theoretical (vivchennya, analysis and synthesis), systemic-sound, practical (bringing theorems).

Historical statement

Trikutnik є one of the central figures of all geometries.

When the establishment is victorious, it is most important for the government.

The power of the tricycle is widely used in practice: in architecture; in case of development of armchair, in case of planning of apartments; in industry, with the design of small details, with the preparation of budget materials, with the development of marine and avia ships; in navigation for laying the correct and most accurate route; in astrology and astronomy, the trikutnik has an even more significant figure; tricycles to use high-voltage power transmission lines and backbones with high-voltage construction.

In addition, there are a lot of spheres, de-stagnate the power of the tricot worker: if you fix the load in the billiards, you need to get the bag out of the tricyt's watch, for the tricky tricky to get a special attachment; placement of pins in the Bowling group near the viglyadi of a single-sided tricycle; for folding beautiful parquet flooring tricytes; attachment of Pascal's tricycle: the skinny number of the back-to-back sum of two numbers above it (circle three numbers with the tricyter). Everything is elementary, altogether there are miracles in this! Pascal's trikutnik computer re-read to MOV Colorah.

The theme of the tricot can be continued unmeasured.

Yakikh tilki trikutnikiv not maє on the light!

There is also a figurative meaning of this figuri: for example, the rule of the "golden tricycle" is based on the psychology of the buyer - if you know the goods you need, the buyer will go straight to the checkout. Zamdannya sellers - zmusiti yogo zatrimatisya in the store more, rostashuvavvshuyu consumer goods in the tops of the obvious trikutnik, so that "anchorite" the buyer. More than the area of the tricycle, we can name the plan of the store in the distance. At the grocery store with anchor goods є gastronomy, dairy products, hlib. The rear end wall of the trading floor є another person for the significance and the very same place to find a comrade-anchor - the very reason for the customer to go through the entire perimeter of the store.

Widely vidomiy Bermudskiy trikutnik - tse district in Atlantic Ocean, In which there are some tamnichi operations of sea and sailing ships. The area is surrounded by lines from Florida to the Bermuda Islands, far to Puerto Rico and back to Floridi through the Bahamas.

The vivchennya of the trikutnik and all the authorities is an even more relevant topic.

The meta given to the robot is to tell us about the signs of equanimity of tricycles, and one of the most important authorities.

Signs of equanimity of trikutniks - tse theorems, on the display of which you can bring,tricytes рівні.

In geometriya vicoristoyu there are three signs of equanimity of tricycles.

The topic is given practically vivchen, so as for this year's day there are three signs of the equanimity of tricycles, proven for additional theorems.

In the distant past, at the same time astronomy appeared science - trigonometry. The word "trigonometry" is rocked from the walnuts "trikutnik" and "mirayu". Literally meaning - "the science about the development of trikutnikiv".

For help, they pulled the tails on with 3, 4 and 5 women, some Egyptian women trimmed straight kuti during the construction of churches, etc.

The art of imaging objects on the land from the Ancient Hours was screwed up to the respect of the people, people painted on the skeletons, walls, sudins and other objects to throw, decorative ornaments, roslini, tvarin. People paused before the image correctly represented the natural form of the object.

Vchenya about the selection of figures on the basis of the theory of common and proportions was established in Ancient Greece in 5-4 centuries before our era and is developed until now. For example, even a lot of childish igrashok to such objects of an over-grown light, swollen and odd of the same style, are allowed to grow up. It’s possible to keep it on and on. I resist, all people are like one to one and how to keep the Bible, opening God for his image and likeness.

Signs of the equanimity of tricycles in Mali are very old and important in geometry, since the proof of numerical theorems was carried out to prove the equilibrium of quiet tricycles. The proof of the equanimity of the tricusters was taken up by the Pifagorians. Behind the words of Prokla, Evdem Rodosky ascribed to Thales Miletusky proof of the parity of two tricycles, both of which were right on the side and two lay down to it (a friend of the sign of the tricky's rivnosti).

Qiu theorem Thales vikoristovuvav for viznennya vіdstanі from the coast to sea ships.In a different way, koristuvavsya when tsyom Thales, just not seen.

Signs of equanimity of tricycles.

It is almost a value. Trikutniks ABC and A1Y1C1 are called rivnim, as it can be done in one piece.

The trikutnik is stored in six elements: three cuts and three sides.

When you have a meal: "Do I need to take the number of elements of a tricycle to establish the equilibrium of two tricytniks?"

It is impossible to establish the parity of two tricycles one element at a time, but it’s impossible: "What will be equal to one element?"

So it is very unwise to establish the equality of two tricycles, vicarists, two elements through the marriage of information for the establishment of equality.

It is possible to establish the equanimity of two trikutniks, vikoristovuchi three elements. Ale with a ts'omu food wine: "Do you need to name three elements in order to establish the equanimity of trikutniks?"

With the introduction of food, I looked at the school handbooks of geometrical authors, as well as vocabulary and presenters. In children of the same class, three signs of equanimity of trikutniks have been proponated to vivchennya only.

Θ1 Sign : If there are two sides and cuts between them of one trike, then both sides and cuts between them are of the same trike... fig. 1

Delivered. Tricytes are visible ABC i A 1 B 1 C 1 , (Fig. 1) for which AB = A 1 B 1, AC = A 1 C 1 ∠ A = ∠ A 1 ... Attainable, but ΔABC = ΔA 1 B 1 C 1.

So yak ∠А = ∠А 1 , Then tricycle ABC can be attached to tricycle A 1 B 1 C 1 so, vertex A is added to vertex A 1 , And the sides AB and AC are imposed on the A 1 B 1 і A 1 C 1. Slices AB = A 1 B 1, AC = A 1 C 1 , Then side AB succeeds from side A 1 in 1 and side АС - from side А 1 C 1 ; zokrem, get points B and B 1, C and C 1 ... Otzhe, get on the side of the sun and b 1 Z 1 ... Otzhe, tricycles ABC and A 1 B 1 C 1 I will get back, it means, the stench of rivn.

And the yak axis in Ancient Egypt The Persha was stuck with signs of ryvnosty trikutnikiv (on both sides and kutu between them), Thales is also the creator of yogo, for vimіryuvannya visoti pіramіdi: clearly, which is worth in front of majestic feast, How can you help it? Do not even dodge it before her! And here, to help Thales Miletsky, come the Persha, a sign of eagerness of trikutniks: in the absence of those who were exactly as young as they were, storing the theorem, it turned out that the time was right (Fig. 2).

Small. 2

Θ2 Signs: If the side and two knots of one tricycle are attached to it, we will rest on both sides of the tricycle, then both tricycles are of the same size.

Proof: Yaksho in △ ABC і △ А 1 B 1 C 1 math mісce takі ravnostі AB = А 1 B 1, ∠BAC = ∠B 1 A 1 C 1, ∠ABS = ∠A 1 B 1 C 1 ... Applied one on one jersey A 1 B 1 C 1 and ABC in such a rank, which were made equal to AB and A 1 in 1 and kuti, who lie down to them. Yak i in the front butt already looked out, if necessary, tricycle A 1 B 1 C 1 it is possible to "turn over and on the back side". Tricutniks are sp_vpadut, otzhe, the stench can be vvazhatsya pivnimi.

Θ3 Signs : If the three sides of one trike are equal to the three sides of the other trike, then these are the same. Proof: Come on for △ ABC і △ A 1 B 1 C 1 fair equanimity A 1 B 1 = AB, B 1 C 1 = BC, C 1 A 1 = CA. Changeable tricycle A 1 B 1 C 1 such rank, side A 1 in 1 from side AB, і vertices B 1 і B, A 1 і A, сівпадать. Vizmemo colo with the center in A and radius AC, and other surroundings with the center B and radius BC. The stake is flipped over at two symmetrical points with the same AB: point C and point C 2 ... Hence, C1 for the transferred tricycle A1B1C1 is guilty of either the points C or C2. Be it vipadku, it will mean parity △ ABC = △ A 1 B 1 C 1 , So yak tricutniki △ ABC = △ ABC 2 рівні (also tricytnyky є symmetrical, as is likely to be AB.

Tse power - the rigidity of a tricycle - is widely victorious in practice. So, close the stop at the vertical position, before putting it on; the same principle is applied when installing the bracket.

The power of the tricycle's rigidity is widely used in practice in case of modern construction.

The third signs of equanimity of tricycles are viplivas, and tricycles is a zigzag figure. To that, it is possible: it is possible to clearly have two slats, in which two ends are scraped with flowers. Such a design is not rough, however, it is destructive or rosy in the form of laths, we can change them. Now, there is one more rail and scryptly, with great finishes of the first two slats. Otrimana design - trikutnik - will be hard. At them it is not possible to destroy any of the two sides, that is, it is not possible to change any one kut. Surely, as far as we were, then we took away a new tricycle, which was not rivvy to the wicked one. Ale tse is unhappy, so yak new trikutnik maє dorіvnyuvati vikhіdnom on the third

To the assistant of elementary mathematics M. Ya. Vigodskiy I know one more sign.

Θ4 Signs: Whenever there are two sides and a hut, how to lie against a large number of them one tricycle is similar to two sides and a kut, which is to lie against a large number of them of a tricot, then these are tricycles.

I'll give you a sign.

given : ΔABC, ΔA1B1C1, AB = A1B1, AC = A1C1,∠ B = ∠ B1

Bring: ΔABC = A1B1C1.

Roztashuєmo trikutniki so, yak on a little one 1. Z'єdnaєmo B і B1, toodі ΔАВВ1

Rіvnobedreniy, otzhe∠ 1= ∠ 2. ∠ 3= ∠ 4 yak surplus rivnyh kutiv.

Otrimaєmo ΔVSB1- displacement, stars BC = B1C1. ΔАВС = ΔА1В1С1 behind three sides.

Also, in the school course, there are 4 signs of equanimity of straight-haired tricycles:

Θ1 ... If the legs of one rectangular tricycle are similar to the same legs, then the same tricycles are equal.

Θ2 ... Yakshho leg and fit to new gostry kut one straight-leg tricycle is similar to the same leg and to the adjacent one to the newest best tricycle, then such tricytes are equal.

Θ3 ... If the hypotenuse and the gostry kut of one straight-handed tricycle is different from the hypotenuse and the gostrom kutu, then the same tricycles are of the same type.

Θ4 ... If the hypotenuse and leg of one rectangular tricycle are both equally hypothetical and the leg of the first one, then such tricycles are equal.

I will show the theoretical base for the signs of equanimity of tricycles, bring it to the sides and codend, vicoristovanim in the classic signs of equanimity of tricycles, the main components: bisectrix, median and height.

Non-standard signs of equality of trikutniks.

1) On two sides and the length is drawn up to one of them.

Given: AB = A1B1, BC = B1C1, AK = A1K1,

Bring: ΔABC = ΔA1B1C1.

Proof: ΔABK = ΔA1B1K1 for hypotenuse and leg, tod∠ B = ∠ B1 і recognizable ΔABC = ΔA1B1C1 for the first time.

2) On two sides and median, held up to one of them

Given: AB = A1B1, BC = B1C1, AK = A1K1, AK і A1K1 - median.

Bring: ΔABC = ΔA1B1C1.

Proof: ΔABK = ΔA1B1K1 for three sides, meaning∠ B = ∠ B1 і ΔABC = ΔA1B1C1 for the first time.

3) On both sides and the height, drawn from the third kut.

Given: ∠ B = ∠ B1, ∠ C = ∠ C1, AK = A1K1.

Bring: ΔABC = ΔA1B1C1.

Proof: ΔABK = ΔA1B1K1 for leg and gostrom kut, meaning BK = B1K1,

ΔACK = ΔA1C1K1 on the leg і of the gostrom kut, meaning KC = K1C1, and also BC = B1C1, and ΔABC = ΔA1B1C1 for another familiarity.

4) Behind the sides and two heights, we will draw from the huts, lying down to the whole side.

Given: AC = A1C1, CM = C1M1, AK = A1K1.

Bring: ΔСC = ΔA1B1C1.

Proof: ΔAMC = ΔA1M1C1 on the leg і hypotenuse, meaning∠ A = ∠ A1, and ΔAКC = ΔA1К1C1 on the leg і hypothenuse, meaning∠ С = ∠ С1.

From the same, ΔABC = ΔA1B1C1 for another acquaintance.

5) On two sides and a line drawn to the third side.

given: AB = A1B1, BC = B1C1, BK = B1K1.

Bring: ΔABC = ΔA1B1C1.

Delivered: ΔABK = ΔA1B1K1 for hypotenuse and leg, meaning AK = A1K1,

ΔBKC = ΔB1K1C1 on the leg і hypotenuse, meaning KC = K1C1.

From the same, ΔABC = ΔA1B1C1 behind three sides.

6) On the sides, one of the cuts extending to the whole side and bisectors of the cuts.

Given: AC = A1C1, AK = A1K1,∠ A ∠ A1.

Bring: ΔABC = ΔA1B1C1.

Proof: ΔКАС = ΔК1А1С1 for the first time I know, meaning∠ С = ∠ С1,

ΔABC = ΔA1B1C1 for another familiarity.

7) On two heights and roses, one of the heights is connected.

Given: CM = C1M1, AK = A1K1, ∠ A ∠ A1.

Bring: ΔABC = ΔA1B1C1.

Proof: ΔAMC = ΔA1M1C1 for leg і gostrom kut, ΔKAS = ΔК1А1С1 for leg і hypothenuse, ΔABC = ΔA1B1C1 for another familiarity.

Visnovok.

In the course of the journey, I am aware of the three main signs of the equanimity of the tricusters, you can count the least of them. I have formulated and in advance the parity of tricycles in terms of median, height, bisectors of the tricycle in the single sides and kutami of the tricycle, which can be seen in the presence of three elements. Now I can tell the students of our school to see the signs of equanimity in tricycles. Tse allow the graduates of the school to save the results of my education during the preparation to the OGE and ADI and it is easy to see the geometric design on the basis of the knowledge.

The result of my message: The introduction of a kilka signifies the eagerness of tricycles, so that one does not get involved in the school course of geometry.

List of Literature

Vigodskiy M. Ya. Dovidnik in elementary mathematics.
Geometry. 7-9 class: navch. For zalnoosvit. installation / L.S. Atanasyan, V.F.Butuzov, S.B. Kadomtsev і ін. - 19th ed. - M .: Education 2009.
Pogorulov A.V. Geometry: Textbook. For 7-9 cl. zagalnoosvit. Install. - 3rd view. - M .: Education, 2002.
... Encyclopedia "Avanta" in mathematics, Moscow, 2004
2. "Vіkіpedіya" - Vіlna encyclopedia.
3. Glazer G.I. "History of mathematics in schools", Moscow, Enlightenment, 1982
4. Gusєva T.M. Signs of similar triangles. - Moscow, Pershe Veresnya, supplement "Mathematics", 1999 r, No. 28
5. Pogorulov A.V. "Geometry 7-9 class",Moscow, Education, 2003 r

Dodatok 1

1.Yak you vvazhate, are there any signs of equanimity in trikutniks?

A) 3 B) more than three C) less than three

2. Would you like to know new signs of equanimity of tricusters?

A) so B) dumb

Instructions

Yaksho at trikutnik_v ABC and the DEF side AB is on the side DE, and the kuti, adjacent to the AB side, will fit to the DE side, then the tricycles will fit in the length.

As for the tricytes ABC side AB, BC and CD are similar to the sides of the tricycle DEF, then the tricytniks are equal.

Beast to respect

If it is necessary to bring the parity of two straight-haired tricycles between oneself, then the price can be made for the help of such signs of the parity of straight-handed tricycles:

One each of the cathetes and hypotenuse;
- on two legs we see;
- one by one from the legs і snug to the new gostry kuta;
- by hypotenuse and one from gostrich kutiv.

Trikutniki are guttrock (as all kuti are less than 90 degrees), obtuse (as well as one kuti is more than 90 degrees), even-sided and straight-sided (as two sides of the yogi).

Korisna is happy

Take care of the tricytes for yourself, and take the tricycles. Podbny trikutniki vvazhayutsya those, in which kuti are equal to themselves, and the sides of one tricycle are proportional to the sides of the other. In addition, it means that if two tricycles are similar to each other, then the price is not a guarantee of their parity. When rozpodіlі of similar parties of trikutnikіv one on one rozpodіlі so ranks kofіtsієnt pіbnostі. Likewise, the efficiency can be set off by way of the length of the area of the other trikutniks.

dzherela:

to improve the parity of the tricycle areas

Two tricycles are equal, as all the elements are one equal to the elements of the one. It is not necessary for the nobility to raise all the tricycles, and to develop them about their parity. To deliver the mother, set the parameters in the assigned figures.

Instructions

If you see two sides of one tricycle of equal and equal sides, then tricycles are visible. To prove the vertices of the rural kutiv two figures. Advance the invoice. For two tricycle points, direct one side of the overlaid tricycle along the outer sides of the lower figuri. For the mind, the sides are in two pounds. It means, the end of the path. Otzhe, I found another pair of tops in the given trikutniki. Straight to the other side of the kut, with a rocket, sp_vpadut in much the same way. And the fragments of the sides of the rivna, the overlapping of the remaining summit will appear. Between two points can be drawn by one straight line. Otzhe, third sides in two triplets spіvpadut. We have taken away two more of the figurians and the persuasion of the Persian sign of the equanimity of the tricusters.

If the side and two kutas are adjacent to it in one tricycle equal to the first one, then two tricycles are equal. To bring the correctness to the correctness, put two figurines, having found the peaks of the ryvny kutiv at the rivny sides. In addition to the eagerness of the paths in the path of directly other and third sides, it is unambiguously to become the point of crossing, i.e. Another sign of the equanimity of the trikutniks of communication.

In the midst of a majestic number of bagatokutniks, which, along the way, is a closed, impenetrable laman line, a tricycle is a figure with the smallest number of kutiv. In other words, the simplest bagatokutnik. Ale, unimportant for all its simplicity, the figure is full of riddles and clues, which hang in a special branch of mathematics - geometrics. To improve the discipline in schools, Vikladati is in this class, and those "Trikutnik" here come with a special respect. Children are not only aware of the rules about posting themselves, but they are, vivchayuchi 1, 2 and 3 signs of equanimity of tricycles.

Perche znayomstvo

One of the first rules that schoolchildren should know about is to sound approximately like this: the sum of the values of all tricycles is up to 180 degrees. To make sure that it is hardened, you can use the help of a protractor to change the skin from the tops and folds of all meaning. Vyhodyachi z tsyogo, with two v_domyh values, it is easy to score a third. by the way: For a tricycle, one of the sides of the road is 70 °, and the first one is 85 °, and what is the value of the third one?

180 - 85 - 70 = 25.

View: 25 °.

Zavdannya can be more foldable, when it is said to deprive one meaning of a kut, but about another value it is said to be less, a little more or less.

For a tricycle, for the purpose of making quiet specialties, they can carry out special lines, I will name my skin:

visota - perpendicular to a straight line, drawn from the top to the opposite side;
all three heights, carried out at once, in the center of the figurine are re-flowing, setting up the Orthocenter, which, in the form of a tricycle, can be transformed into the middle, as well as the call;
mediana - line, which is the top from the middle of the opposite side;
peretin median є the point of this gravity, is located in the middle of the figuri;
bisector - line, which goes through the vertex to the point of overflow from the opposite side, point overflow of three bisectors є by the center of the inscribed stake.

Simple truths about trikutniki

Trikutniki, yak, vlasne, and all figurines, conceal their specialness and power. Yak already spoke, tsya figura є with the simplest bagatokutnik, and with its own characteristic signs:

against the side you found, lay a kut of greater size, and navpaki;
lie on opposite sides rivnі kuti, Butt to that - tricycle;
the sum of the internal kutiv depends on the road 180 °, which is already shown on the butt;
with the advancement of one side of the tricycle for the first line, a call will be established, which will be dorіvnyu sumi kutiv, not crazy with him;
Be it from the side, you will be less than the sum of the two sides, more of them.

vidi tricutnikiv

The offensive stage of knowledge of the polyagaє at the designated group, prior to which the performances of the trikutnik are introduced. The thickness of the tricyt cutter is so high that it can be found in the size of the tricycle cut.

Rivnobedreniy - with two equal sides, which they call bichny, the third in the whole range is presented by figuri. Kuti was the basis of such a tricycle, but the median was drawn from the top, by a bisectrix and by a height.
A correct, or even an equilateral trikutnik, is the price of one, at which all sides are equal.
Rectangular: one of the yogo doorways 90 °. The side opposite to the cuff is called the hypotenuse, and the two sides are called the legs.
Gostrokutny trikutnik - all kuti less than 90 °.
Obtuse - one of the slopes greater than 90 °.

Equality and suitability of tricycles

In the process of navchannya not only look around but take a figuru, but break two tricycles. І tsya, good luck b, simple theme I have mastered the rules and theorems, for which it is possible to bring the figuri to look at. Signs of equal importance for tricycles are also valid: tricycles are of equal importance. With this parity, if you put two figurines one on one, all the lines will go. Likewise, figurines can be podbnimi, zokrema, they tend to be practically the same figurines, which grow in size. In order to create such a story about performances by tricycles, you need to look at one of these minds:

two kutas of one figuri rivni two kutas of the one;
two sides of one are proportional to the two sides of another tricycle, and the size of the kutiv, approved by the parties, is equal;
the three sides of the other figuri are the same as in the first.

Obviously, for transverse efficacy, as it is not more vicious than normal summaries, it is necessary to have the same meaning of all the elements of both figures, however, it’s important to say goodbye to the theorem’s victories, and to prove the dichotomy of the tricycle.

First sign of equanimity of trikutniks

The head of the department is based on the brought theorems, as it sounds like this: "Like two sides of a tricycle and a cut, which stench, take two sides and a cut of another tricot, then both sides of a tricycle and a cut."

How does it sound to be proved by theorems about the Persha sign of equanimity of trikutniks? All in all, there are two types of rivnas, like the stench of the same dozhina, or the circumference of the rivni, which may be the same radius. And in vipadku with trikutniki є there is a sign, mayuchi yaki, it is possible to let it go, but figurine is identical, but it can even be victoriously victorious in case of viral geometrical problems.

Yak sound theorem "The first sign of equanimity of trikutniks" is described by vishche, and the її axis is proved:

Supposedly, tricycles ABC and A 1 B 1 C 1 may be the same sides AB and A 1 B 1 and, apparently, BC and B 1 C 1, but the cut, which is adopted by the same sides, may be one and the same value, so that it is equal. Todi, inserting △ ABC on △ А 1 В 1 С 1, can be seen from all lines and vertices. Zvidsy vipliva, scho tricytes are absolutely identical, and that means they are equal to themselves.

The theorem “The Persha of the Sign of Equality of Tricutniks” is called “On two sides and kutu”. Vlasne, in general and polyagaє її is the essence.

Another meaning theorem

Another sign of eagerness is to be brought in the same way, to prove to be grounded on the fact that, when the figures are applied, one on one stench will rise behind all the peaks and sides. And the theorem sounds like this: "As one side and two kuti, in the established ones take care of the fate, see the parties and two kutas of another tricycle, then the figures are identical, to be equal."

Third sign and proof

Yaksho yak 2, so і 1 sign of equanimity of tricycles is stosuvsya yak sides, so і kutіv fіguri, then the 3rd is carried out only to sides. Otzhe, the theorem is beginning to formulate: "If all sides of one tricycle are equal to three sides of another tricycle, then the figure is identical."

In order to bring the theorem to the end, it is necessary to get more detailed attention in the very meaning of equality. By the day, what does viraz mean "tricutniks of rivnі"? Identity to talk about those who put one figurine on the bottom, all the elements fall back, but they can only be in that vipad, if their sides and cut will be equal. At the same hour there is a kut, a prototype one of the sides, as well as at the other tricycle, there will be an emerging summit of another figurine. Slid to mean that in a whole mice it is easy to translate proof into 1 sign of triviality. If such a post-date is not spared, the parity of tricycles is simply unhappy, behind a vignette of quiet vipads, since the figure is a mirror image of the first.

rectangular tricycles

In budovi such trikutniks have є peaks with a kuta value of 90 °. To this, the offensive firmness is fair:

tricycles with a straight edge of the pivot, like the legs of one identical to the legs of the other;
figuri rivni, as well as rіvnі іх hypotenuse and one of the legs;
such tricycles are of equal importance

To bring the theorem into account, add one to one figures, as a result of which the tricycles are folded with legs so that there are two straight lines on the sides of CA and CA 1.

Practically storing

In most cases, in practice, there is a persuasion of signs of equanimity of tricycles. As a matter of fact, it’s a simple matter for the 7th class of geometry and planimetry to be used for calculating the amount of money, for example, a telephone cable without fixing the balance, which will pass through. For the help of the theorem, it is easy to break necessary resources for visiting the island, where it is located in the middle of the river, not overflowing into a new one. For fixing the parkan, having rasped the bar in the spill like that, you won’t split it into two tricycles, or if you could use the folding elements of the robot in the carpentry, or when the crocheted system was set up until the wake-up hour.

The first sign of equanimity in trikutniks is wider in the real "grown-up" life. hocha in school rock The very theme for the bagatokh is boring and unnecessary.