Irregularity of tricot fabric is one of the most important geometrical facts - document
Geometric irregularities.
Under the hour of learning mathematics, learners often have to stumble over the unraveling of inconsistencies. One of the most common types of irregularities isgeometric. At the school, there is little time for perfection, and then the hour of work with similar inconsistencies in the school is blamed for difficulties. However, at the entrance examinations to the VNZ and at the mathematical olympiads of this kind, you can often finish the challenge. Let's look at the deeds of them.
The unevenness of the tricot
Theorem (uneven tricot):
Skin the side of the tricoutnik is less for the sum of the two other sides.
Respect. Other vicorists also and sometimes formulate these theorems, including, of course, the virogenous tricot:
Dovzhinabe-like The side of the tricoutnik will never outweigh the sum of the dozhins of the two other sides.
Respectfully, that the difference between the two by guiding the flooring formulas is insignificant, that there is no sense to look at them perfectly. Nadalі pіd pіd hіvіshennya zavdannya mi vikoristovuvatimem as the first formulation of the theorem, and another, not numbly okremo.
The unevenness of the tricot vinikla, calling for everything, is the same, if a person has learned to walk and even if it’s thought. It seems that the first of these formalizations is to induce Euclid in the famous "Cobs". There you can bring the unevenness of the tricoutnik in such a way. At the same time, the theorem is brought to the attention of those who have the outer kut of the tricouter more than the inner kuta, from which it is summed. From it, a theorem can be deduced from that, against the larger side of the tricutnik, there is a larger inner kut. Dalі, the path of the protilazhnogo to bring the theorem to the fact that there is a large side against the greater inner kut of the tricot. And from the point of the theorem, the unevenness of the tricutnik is shown. The axis is such an uneasy logical language for proving the obvious, it would seem, unevenness!
Theorem proof . Look at trikutnik ABC and show that AB AC + BC. For proof, we are speeding up with one of the types of supplementary motives - in the case of equal vіdrіzkіv ( straightening method).
Have trikutniku ABC(fig. 1) on the selling side BC vіdklademo vіdrіzok CD, equal AC. AT rіnofemoral tricoutnik ACD 
. Have trikutniku ABD kut adb less kuta bad to mean, BD AB, or BC + CD AB. ale CD = AC to mean, AC + BC AB.
Respect. To return the respect, that, based on the formulation of the theorem, we should write down three inconsistencies in a row:
AB AC + BC ;
AC AB + BC ;
BC AB + AC .
Often, having written down one irritability, I forget about the other two. Remember what you can bring to unacceptable pardons.
The unevenness of the tricot can be one of the simplest criteria for membership of three points of one straight line. Three points will lie on the same straight line, or less or less, as evenness can be reached by the unevenness of the tricutnik. Obviously, equivalence can only be reached in one of the three irregularities (divine respect), but one point lies clearly between the other two.
Let me know that the skin side of the tricoutnik is larger than the difference of the two other sides.
Let's put it like a buttstock of the unevenness of the tricutnik of the kilka of a pair of awkward geometric zavdans.
(a , b , c - Side trikutnikABC ).
a ( b - c ) 2 + b ( c - a ) 2 + c ( a - b ) 2 + 4 abc a 3 + b 3 + c 3 .
a , b іc
a , b іc - Dovzhini storіn dovіlnogo trikutnik. Bring what
( a + b - c )( a - b + c )(- a + b + c ) abc .
a, bі c- Dovzhini storіn dovіlnogo trikutnik. Bring what
a 2 b (a - b ) + b 2 c (b - c ) + c 2 a (c - a ) 0.
Longen the two sides of the tricot a and b please the minds a b, and longen the heights similar to them hai hb.
Bring unevenness a + ha≥ b + hband signify, if equanimity is attainable.
To bring, what is the sum of dovzhins, if there are two medians of a good trikutnik
a) no more than ¾P
, deP
- the perimeter of this tricoutnik;
b) no less than ¾p
, dep
- Napіvperimeter tsgogo trikutnik.
Solution
Let's have a look CB 1 so, scho chotirikutnik ABB 1 C– parallelogram, todi AC=BB 1 . 3 trikutnik BB 1 D we accept that BB 1 +BD B 1 D i, otzhe, AC+BD B 1 D. Remembrance is over, scho trikutnik CB 1 D equilateral ( CD=CB 1 = 1 , a B 1 CD=AOC= 60 o ), i, later, B 1 D= 1 . In this manner, we take AC+BD 1 .
Solution
Take it to the side AB, BC, CA points C 2 , A 2 , B 2 so what A 1 B 2 | AB, B 1 C 2 | BC, C 1 A 2 | CA(Rice.). Todi A
1
B
1
A
1
B
2
+
B
2
B
1
= (1 - )
AB
+ (2 - 1)
CA. Similarly B
1
C
1
)
BC
+ (2 - 1)
ABі C
1
A
1
)
CA
+ (2 - 1)
BC. Adding up the unevenness, otrimuemo P 1 P.
It's clear what A 1 B 1 + A 1 C B 1 C, then. A
1
B
1
+ (1 - )
BC
.
CA. Similarly B
1
C
1
+ (1 - )
CA
.
ABі C
1
A
1
+ (1 - )
AB
.
BC. Adding up the unevenness, otrimuemo P 1 (2 - 1)P.
Mathematical group of the Rusaniv Lyceum
The unevenness of the tricot
The unevenness of the knitwear is one of the most important geometric facts. As one of the intuitive powers of the state, it often helps to overcome difficult geometric and textual tasks. For the help of the unevenness of the tricot, it is possible to add some of the possible options for refinishing any elements in bulky geometric problems. Often, the very nevikonannya of the unevenness of the tricot (and the very reach of the new equanimity) gives a strong indication of the reliability of the three points of one straight line. In this way, the unevenness of the tricoutnik is at the same time intuitively sensible, obvious, but often becomes a straining tool when solving serious mathematical problems.
Dekilka slіv about nerіvnostі
In mathematics unevennessє assertion about the visible value, or the order of the two objects that are looked at, or about those that are simply not the same. Classical unevenness, as an object of follow-up, can also be seen as an example of a change in order. Separate strictlyі non-suvori nervousness. Otherwise, moving on to the language of speech, suvore inconsistency can be taken into account in terms of a strict order on the impersonal real numbers (that is, in order to establish the power of antireflexivity, antisymmetry and transitivity). If we talk about the non-suvorability of unevenness, then we can talk about it as about the introduction of a non-strict order on the same multiplicity (in order to look at the place of anti-reflexivity and reflexivity). Guess what about the blue as a mathematical object and their power was already guessed in Lecture 7 (they looked at the power of the dilemma). We can report on their work in the future, and the stinks of the stink can be successfully systematized and explained a number of elementary mathematical ones to understand. Now we will introduce a sprinkling of examples of skin irregularities from the names of types. Suvorimi Neurivities are called such nerivities:
- a < b- means that alessb; a
> b
- means that amoreb; a
≠ b- means that anot goodb but what aі b different.
- a ≤ b- means that aless than oneb otherwise, what are you, ano more (do not revisit, do not revisit)b; a ≥
b- means that amore than oneb otherwise, what are you, ano lessb.
The unevenness of the tricot
Theorem (uneven tricot): Skin the side of the tricoutnik is less for the sum of the two other sides. Respect. Other vicorists also and more often formulate these theorems, including, of course, and the fall of the virogenous tricot: Dovzhina be-like The side of the tricoutnik will never outweigh the sum of the dozhins of the two other sides. Respectfully, that the difference between the two by guiding the flooring formulas is insignificant, that there is no sense to look at them perfectly. Nadalі pіd pіd hіvіshennya zavdannya mi vikoristovuvatimem as the first formulation of the theorem, and another, not numbly okremo. The unevenness of the tricot vinikla, calling for everything, is the same, if a person has learned to walk and even if it’s thought. It seems that the first of these formalizations is to induce Euclid in the famous "Cobs". There you can bring the unevenness of the tricoutnik in such a way. At the same time, the theorem is brought to the attention of those who have the outer kut of the tricouter more than the inner kuta, from which it is summed. From it, a theorem can be deduced from that, against the larger side of the tricutnik, there is a larger inner kut. Dalі, the path of the protilazhnogo to bring the theorem to the fact that there is a large side against the greater inner kut of the tricot. And from the point of the theorem, the unevenness of the tricutnik is shown. The axis is such an uneasy logical language for proving the obvious, it would seem, unevenness!|
|
. Have trikutniku ABD kut AD.B. less kuta bad to mean, BD > AB, or BC + CD
> AB. ale CD = AC to mean, AC + BC > AB. Respect. To return the respect, that, based on the formulation of the theorem, we should write down three inconsistencies in a row: AB < AC + BC; AC< AB + BC; BC < AB + AC. Often, having written down one irritability, I forget about the other two. Remember what you can bring to unacceptable pardons. The unevenness of the tricot can be one of the simplest criteria for membership of three points of one straight line. Three points will lie on the same straight line, or less or less, as evenness can be reached by the unevenness of the tricutnik. Obviously, equivalence can only be reached in one of the three irregularities (divine respect), but one point lies clearly between the other two. right. Let me know that the skin side of the tricoutnik is larger than the difference of the two other sides. Let's put it like a buttstock of the unevenness of the tricutnik of the kilka of a pair of awkward geometric zavdans. Head 1. Bring what the happy chotirikutnik has ABCD AB + CD < AC + BD. |
|
AO + OB > AB;
CO + OD > CD.
Let's look at the sum AC + BD:
AC + BD = (AO + OC) + (BO + OD) =
= (AO + BO) + (OC + OD) > AB + CD.
Manager 2. Tell me what the trikutnik has ABC Vikonano Nerіvnіst ( a, b, c- Side trikutnik ABC). Solution . We are speeding up the following from the unevenness of the tricutnik (div. to the right):
(Let's assume that 
). Todi, sounding into the square of insulting parts of the nervousness, we take away: Similarly:
;
.
Adding up all three inconsistencies, we take away the need. right. Tell me what the median AM at a pretty knitter ABC for a dozhina less, lower 
. Manager 3. A square is given on the plane ABCD i mottled O. Tell me what you see at the point O up to one of the vertices of the square I do not overwhelm the sumi O up to three other vertices of the square. Solution
. Store the unevenness of the tricot AC + OC > OAі OB + OD > BD. so yak AC = BD, then, quickly, we need it. Head office 4. Find a point in the middle of a swollen chotirikutnik, such that the sum of steps in it to the tops is minimal. Solution
. So like a chotirikutnik is bulging, the yogo diagonals are tinted in dots O middle of the new. Significantly, the peaks of the Chotirikutnik through A, B, Cі D(behind the year's arrow). Todi sum vіdstaney vіd O up to the tops of dorivnyu sum_ dozhin diagonals ACі BD. Ale for any other point P maybe, first, what a sum of money P up to the top no less AC + BD, but in another way, or PA + PC > AC, or PB + PD > BD. Otzhe, tsya sum dorivnyuє AC + BD only once P run with a dot O. Mean point O- Shukana. Nerіvnіst trikutnik successfully zastosovuєtsya y dosit tangled text problems. Well, such plants can have a lot of deposits, in addition, far away you will encourage a geometric interpretation. Head office 5. The deyakіy kraїnі roztashovanі 4 places: A, B, Cі D. Two letaks flew out of the city at the same time A. The route of the first flight: A-B-D-C-A-D-B-C-A, and the route of another: A-B-C-D-A-B-C-D-A-B-C-D-A. Which of the planes finish your route earlier, if so, how fast are the same? Don't be afraid to experiment! Even though the task does not specifically specify the distribution of objects, You have the right to paint in your own solution everything that does not superchit your mind - even if it is yours. In addition, the places in Task 5 you can arrange as appropriate. It is necessary to remember that after deciphering the “normal”, infamous depression, it is necessary to sort out “pathological” deeds, okremi depressions. For example, at Zavdanny 5, you may need to look at the vapadka, if three places lie on one straight line, everything should lie down as a solution for a wild vapadka. Solving problems 5
. Let's write down the routes of the dermal treatment as a sum of steps between the places. Dovzhina route of the first flight
Another light to fly through
Let's look at the difference between the first flight, that one has flown the first flight, that one will see, as if the other one has finished.
It is reported that it is not necessary to check the point of expansion A, B, C, D on the flat (mist A, B, C, D borders) will be positive. For whom, look at two views. 1. It is acceptable that the points A, B, C, D ABCD with diagonals ACі BD. Then we write down in sequence the unevenness of the tricutnik for the tricutniks ABC, BCD, CDAі DAB(div. Fig. 2):
AB + BC > AC;
BC + CD > BD;
CD + DA > CA;
DA + AB > D.B..
Having crushed all the nervousness, we take it away
2. We can look at the vipadok if the dots A, B, C, D create on the square chotirikutnik ACBD with diagonals ABі CD (Paint your own little ones). It is worthy of note that the nervousness of the tricutnik is beaten up quieter than the tricutniks themselves, that at first glance. It appears that the solution of the task will be left to them, regardless of those that the task of resolving the dot on the square has changed. Tse can vvazhe sche one characteristic rice rich rozv'yazkіv tasks, scho vykoristovuyut nerіvnіst trikutnik. Otzhe, the first flight to arrive earlier, the oskіlki yogo route is shorter than the route of the other. Respect that the opening of Task 5 will require a little analysis, which is not an authoritative quality of all Olympiad tasks. Be respectful - your vision will only be correct if you look at all possible fluctuations that fit your mind. It also means that often on the little one, which depicts the mind's tasks, the tricutnik is not visible, the stoppage of the nervousness of the tricutnik would give an instant solution. Such a time can be helped by a successful selection of a geometrical transformation. Let's talk about tse mi troch by the goda. Acquaintance with the nervousness of the tricot worker at whom we next should be finished. Ale nova zustrіch from him is just around the corner. Grade 7 Lecture 13
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The video lesson "The unevenness of the tricot" reveals the proof of the theorem about the unevenness of the tricot. The task of this video lesson is to make it easier to remember the theorem and the consequences of it, to understand that memory of the mismatch for the її proof.
High respect for the accuracy of the material, voice support gives the opportunity to win as an independent part of the lesson, increasing the teacher’s hour for the enrichment of the quality of learning, strengthening the individual work with the students.
The video lesson starts with the presentation of the theorem about the unevenness of the tricutnik. For memorization, the confirmation of Vaughn's theorem is shown on the screen in color. Tsya theorem stverdzhuє, scho whether the side of the tricoutnik is smaller in the sum of two other sides. The proof of the confirmation is shown on the butt of the tricot Δ, which is demonstrated under the text of the theorem on the screen.
It is clarified that in order to prove the theorem it is necessary to confirm that the side AB is less than the sum of the sides AC and CB. This date is marked on the screen with virase AB Having mastered this theorem, you can see a corollary, which seems to be true, that for any three points A, B, C, if they do not lie up to one line, just irregularities: AB The video lesson “The inconsistency of the knitter” can be used by the teacher in the lesson of geometry as an educational help, or as part of the lesson, the deputy is explained by the teacher of the new topics. Let’s learn in more detail the explanation of the teacher in case of independent teaching of the subject, and help explain the subject further for the hour of distance learning. meta lesson: vivchit the theorem about the unevenness of the tricot and show її zastosuvannya at the hour of the cherry day. Manager: lesson type: a lesson in learning that primary consolidation of new knowledge. Ownership: whiteboard, computer, interactive whiteboard or multimedia projector, presentation, assistants, worksheets ( Addendum 1
), 14 sets of cardboard sleeves of 5 cm, 7 cm (2 pcs.), 9 cm, 12 cm, 14 cm, 16 cm, plates with tricots, smiley ( Addendum 2
). HID LESSON 1. Organizational stage 2. Preparation before the main stage of the lesson(Safety of motivation and acceptance by scientists of the beginning and learning activities, updating of basic knowledge) - Marvel at the little ones, the victors on the doshtsi. How is it called to post? (Tse trikutnik.) 3. Acquisition of new knowledge and methods 3.1. Statement of the problem, drawing up a hypothesis Yakby only slept me, De volcanoes shabby the sky – The Miracles of Anatoly Starikan are consecrated to our little fatherland of Kamchatka. Kamchatka has its own traditions and one of them is Beringia. - Call the Beringia to be held near the birch and at once from the ear of spring to come to the settlements on their way, bringing joy to their sacks. Varto respect that the race, the crime of the warehouse, is of the most humanitarian significance for the inhabitants of the villages and villages of the Kamchatka Territory, deem the participants of the races. Children and schools in distant places in Kamchatka are given sponsorship assistance. Problematic situation. Is it necessary to encourage a figure to solve this problem? (It is necessary to call a tricoutnik.) How can a third party dovzhina? Hang your hypotheses, we will check them like a lesson. Last job - In front of you lie the layouts of the sides of the knitwear. a) 7, 12, 9; It is easy to induce a tricoutnik to the first manager. The other wiyshov has a vіdrіzok. Why? (T.K. Three vertices lie on one straight line, and a tricutnik is a whole figure, folded from three points, so that it does not lie on one straight line, in pairs with two vertices. - Chi can you encourage the trikutnik at the third vipadka? (It is not possible to induce a trikutnik to the third one, because the dozhina of the larger side is larger for the sum of the dozhins of the smaller sides.) Reader of the vislukhov version of the textbook. In times of folding, you can ask the children to split the double side, prompted by the first and the sum of the two other sides of the tricot. - Ozhe, trikutnik, from what sides could we induce? (Trikutnik with sides 7, 12, 9) AB< BC + АС,
so yak 9 cm< 7 см + 12 см Learn to designate the sides of the tricot, write down the unevenness of the zoshit. – How are virazi called, written on doshts? (Nerіvnostі.) Energizator Open pens, turn bets one by one. Rahunok "one" raise the right hand with a curved pointed finger. On the “two” rahunok, cover the susida’s pointed finger with the left side. At rahunok "three", take your hand and grab your finger susida. Start! The boys are right to win out of satisfaction, as if they know the pressure and create a benign atmosphere, promoting the energy potential of the students. 3.3. Theorem proof - Open the assistant on the side. 74, read the formulation of the theorem about the unevenness of the tricot. Learn to work on the formulas of the theorem, to explain what is given and what is necessary to bring, to be small and to bring the theorem together with the teacher at zoshity. Vіdpovіdat on the question of the teacher. Theorem. The skin side of the knitwear is smaller for the sum of the two other sides. 4. Physical culture, repetition Peremozhtsem Beringії in 2011 became a musher of the Karagіnsk district, and to learn about it, we will help you in the mathematical field of miracles. Know the answers to my question on the little ones, roaming around the perimeter of the class, and name only a letter. (Boys play standing.) - Fully verno, the helper is Andriy Pritchin, who has lifted all the way for 90 years. 5. Primary revision of knowledge and knowledge - Viberіt, yakі tricoutniks do not know? (Learn to practice independently, one person practices white dots, then reverb.) Vidpovid: do not base tricots with numbers 3, 5, 6 - Boys, what did you remember? How to quickly zastosuvat the theorem about the unevenness of the tricot? (Have your own versions.)- The sum of two sides, can be greater for the third side. For example, 10 + 3 > 5, but you can’t make a trick, why? (Oskilki 3 + 5< 10.) То есть, для того
чтобы быстро проверить существует ли
треугольник, надо сравнить большую сторону с
суммой двух меньших сторон. - Well done, lads! Shvidko ran into the zavdannyam! 6. Compilation and systematization of knowledge(solving the problem, revising the hypothesis) - Otzhe, as a Umov can win, so that you can wake up a trikutnik? (The large side of the trikutnik can be smaller in the sum of two smaller sides.) Addendum task:іzkakoy sredný shvidkіstyu collapsed remozhets, yakscho the whole route of wines podolil for 90 years? 7. Setting up a home task 8. Podbags for the lesson, assessment of knowledge, reflection For frontal education, the teacher at once, from the students, gives the bag to the lesson and put marks for the active lads. - What topic have you learned today? (Nerіvnіst tricoutnik.) - Well done! Andriy Pritchin, as a great helper of Beringia, and I am enthralled that I will become a helper for you in this other gallery. Golovne dozhe want and reach the delivered mark. Literature: Atanasyan L.S. that in. Geometry 7-9.: Navch. for lighting fixtures / L.S. Atanasyan, V.F. Butuzov, S.B. Kadomtsev ta in - M.: Prosvitnitstvo, 2006. Internet resources: From geometry, we know that the sum of the two sides of the tricot is not less than the sum of the one of the third side. We wonder how it is possible to state the theorem algebraically. Let's look at the tricutnik, rotting it like it is shown in fig. 22. Geometric irregularity similar to the algebraic irregularity of the tricot How can you bring the rest of the nervousness without going back to geometry? At § 8 goal. III, a proof was given for a one-dimensional variation (div. Theorem 2, Chapter III). in what kind of nervousness looks like this: in this record, it will sound more often, the unevenness is equal to it The simplest way to prove the two-world variant of the unevenness of the tricot (4.50) is to bring the unevenness to it equally strong. Rice. 22. Uneven tricot. For which we are offended by part of the unevenness (4.50) at the square, with which we come to the unevenness equal (4.50). It’s easy to fight, that the rest of the nervousness of one’s heart is equal to the attack: Ale tse nerіvnіst є let's forgive the last in the vіdomoї nerіvnіstі Koshi [two-world option, div. (4.38)] scho th to bring the nerіvnіst trikutnik. As if in a one-sided mood, the minds of the mind, for which the unevenness of the tricutnik (4.50) turns into jealousy, not to become especially difficult. Guess what the unevenness of Cauchy (4.52) can reach equally or less, if proportional, then if the unevenness (4.51) can be taken away by the way of the square root of both parts of the unevenness (4.52). Tsya operation is legal, to that which is on the verge of an invisible square root of virazu, which costs evil. Give the negative square root of the virazu, which stands at the right side (4.52). And here you can find the same, if proportional, in (4.51) there is a lot of unevenness. In this way, evenness (4.51), and also, in the unevenness of tricot (4.50) can be reached only and only if there is a non-negative proportionality coefficient. Use the geometric sense, which is necessary and sufficient for formula (4.50) to have little space for evenness, lying in the offensive: the points (Fig. 21) are due to lie on one straight line, moreover, the points are folded on one side of the point O. the breech is straight. Otherwise, hanging, the points lie on the same line with the point Pro, and lie on the same exchange with the cob Pro. It is easy to get overwhelmed in what the minds of the minds are able to use with different minds for a one-world attitude (irregularity and evenness can be reached even and only if the numbers may have one sign. The proof of the unevenness of the tricot can be taken, following the same path, which, when seen Hölder's nervousness, but to bring to her own mind that the nervousness there may be a place for any real meaning, and, like before, equality is attainable in that and less so, if the number of proportions and the coefficient of proportionality are positive. We turn to the point of nervousness in the goal. VI, de bude will look at this geometric meaning. Let's move on to another proof of the unevenness of the tricutnik, as it is possible to win the same for otrimannya more outrageous results. May the sameness be Irregularity of Kosh in the form, which is the victor's square root [div. (4.51)].
- How to post is called a trikutnik? (Trikutnik is a figure, which is made up of three points, which does not lie on one straight line and three winds, which combines two points in pairs.)
- What do you blame your memory for? What can you tell about this tricoutnik? How to recognize the ABC trickster, to name the great side. (Boys say the teacher's food.)
- And why did I urge you to guess this figure? (Vivemememo is the power of trikutnik.)
- It is quite true, today we are in the power of the "irrivality of the tricutnik".
I would vіdpovіv borderline short,
What is more beautiful than the Earth
I enigmatic, lower Kamchatka.
Low to the bottom lava,
De merging buval and nebil,
І de on zrіst people grass.
- Boys, what about Beringia? (This is a traditional dog sled race that has been held since 1990.)
This year Beriginya was born from 7 to 21 birch.
Beringia started from the village of Esso, and one of the points of the zupinka was the settlement of Tigil. Vіdstan mіzh tsimi settlements 443 km. Farther the mushers went to the village of Ossora. On the other side of the village of Esso, you can see the settlement of Ossora, which is between the settlement of Tigil and the settlement of Ossora 507 km?
Uchnі vіdpovіdat on the teacher's inquiries, buduyut tricutnik at the worker's zoshitі that vyslovlyuyut their hypotheses, for example, vіdstan mizh s. Esso and Ossora are less than 950 km.
The main figure in the examined problems is trikutnik. I am convinced that you are more careful. Tell me, where did you get tricot forms in everyday life? In architecture? (The sign of the emergency tooth is thin. The dahi is making a three-dimensional shape.)
- You're making a move. The basis of the dahіv is laid down by the frailty of the horizontal beams, yakі z'еdnаnі mіzh themselves utvoryuyut trikutnik.
Let's construct mock-ups of good breaths. To show that the women, like lying in front of you, are the beams for waking up the house.
Please, vikoristovuyuchi tі models trikutnika zі sides:
b) 7, 14, 7;
c) 5, 16, 7.
Virna version of children:“If the side, prompted by the first, is less than the sum of the two other sides, then the tricutnik will be.”
ND< АВ + АС, так как 7 см < 9 см + 12 см
AC< АВ + ВС, так как 12 см < 9 см + 7 см.
– What do these three inconsistencies cause? (The sides of the tricot.)
- What is the topic of the lesson? (Nerіvnіst tricoutnik.)
– Formulate your power. (The skin side of the knitwear is smaller for the sum of the two other sides.)
- Well done lads, they did a good job, but in the future, a serious robot to prove the theorem.
Given: Δ ABC.
Bring: AB<АС+СВ
Proof:
There will be an SM air vent, which is more expensive for the CB air supply on the prod- uct side of the AU.
For rіnofemoral ΔVCM ∟1 =∟2
(for the power of kutiv at the equal-femoral tricoutnik).
∟1< ∟АВМ, то ∟2<∟АВМ.
Let's take a look at the tricot AVM.
- What kind of spіvіdnoshnennyam povyazanі side ta kuti? (The trikutnik opposite the big kut has a large side.)
- What side to lie against the AVM? (AM side)
- Yaka side lie against kuta 2? (side AB.)
- Align sides AB and AM? (AB< АМ)
AB< АМ
AB< АС + СМ
AB< АС + ВС
Similarly, it can be argued that the sun< АВ + АС;
АС < АВ + ВС. Теорема доказана.
Do not hesitate to carry out the proof of the theorem verbally, and then write down the proof on the dots in the working papers.
- What kind of tricoutnik is even-femoral? (P)
- Which knitter has a bigger kut? (R)
- Which tricoutnik has a smaller side of the PS? (I)
- What kind of straight-cut knitter has the leg VC, hypotenuse BC? (T)
- What kind of trikutnik is stupid? (H)
- For a straight-cut tricot MNT, name the cut to lay the TM leg (L N)P
R
І
T
H
І
H
- What problem did I put before you on the cob of the lesson? (Beringіya started from the village of Esso, and one of the points of the zupinki was the settlement of Tigil. Between these settlements 443 km. Farther kayuri went to the village of Ossora. )
- Promote the solution of the problem, vikoristuyuchi new knowledge. (Walk between Esso and Ossoroy may be less, below 950 km.)
- What kind of hypothesis did we hang? (Walk between Esso and Ossoroy may be less, below 950 km.)
- What was the hypothesis confirmed? (So.)
- What new things did you discover at the lesson? (Whether the side of the tricoutnik is less for the sum of the two other sides.)
- Did you repeat the trikutnik to the authorities? (A tricout on the opposite side has a larger kut, and back. In a straight-cut tricout, the hypotenuse is larger for the leg. Like in a tricout, there are two equal cuts, then a tricout of equal thighs.)
- What is the name of the dog sled race? (Beringia.)
- From which village do you start? (From the village of Esso.)
- Which village has a finish? (Near the village of Ossora.)
- What is the name of the 2011 rock? (Andriy Pritchin.)
- What goals did we put on the cob of the lesson? Have you reached them? Did you solve the problem of your life?
- What kind of problems did you have in the classroom? How did you get them? What made you think about the topic of the lesson? (Boys give food to the teacher, take part in reflection.)
- And now, once again, focus on your feelings and emotions, on how much the topic of the lesson made you understand, take an appropriate emoticon ( Addendum 2
), and hang yoga on the board.
- Dakuyu, lads, for the work! The lesson is over, goodbye! I succeeded and I overcame you.
