Quadrangle le dikhutlo e nepahetseng - ke chelete ea dikhutlo tsa sekhutlonne ka ...

E mong oa litaba tse thahasellisang ka ho fetisisa e le geometry ea selemo sekolong - ke "sekhutlonne ya" (Kereiti 8). Tsa mofuta ofe lipalo teng, seo e khethehileng litsobotsi tsa botho ba rua? Se ikhethang ka quadrangles le dikhutlo tsa likhato mashome a robong? A re ke re sheba tsohle ena.

Seo jeometeri palo e bitswang quadrangle

Dikhutlontsi hore bopilwe mahlakoreng a mane, ka ho latellana, ba divertise a mane (likhutlong) ba bitsoa ka quadrangles Euclidean thutatekanyong.

Thahasello historing ea mofuta ona wa lipalo lebitso. Ka puo ea Russia ea lereho "sekhutlonne" le tsoa ho "likhutlong tse 'nè" dipolelwana (ka tsela e tšoanang e le "triangolo" - the dikhutloteng tse tharo, "khutlotlhano" - dikhutloteng tse hlano, joalo-joalo ...).

Leha ho le joalo, ka Latin (eo ile a tla ka ho kena lipakeng tsa mantsoe a mangata thutatekanyo ka lipuo tse ngata tsa lefatše) e bitsoa sekhutlonne. lentsoe lena ke ho sebediswa makgetlo a Quadri (a mane) le latus lereho (lehlakoreng). Kahoo, re ka etsa qeto ea hore ba boholo-holo khutlontsi ena o ne a tsejoa feela e le "sekhutlonne".

Ka tsela eo, lebitso la ka (ka khatiso e etsoang tabeng ho ba teng ha mekhabo ea mofuta ona e mahlakoreng a mane, ha likhutlong) bolokoa ka bang lipuo tsa kajeno. Ka mohlala, ka Senyesemane - sekhutlonne le ka French - quadrilatère.

Ka lipuo tse ngata Maslav mefuta ena e tsejoa litšoantšo a ntse a le palo ea likhutlo, e seng mahlakoreng. Ka mohlala, ka SeSlovak (štvoruholník), ka Se-bulgaria ( 'chetiriglnik ") ka Belarus (" chatyrohkutnіk ") ka Seukraine (" chotirikutnik "), ka Czech (čtyřúhelník), empa ka quadrangle Poland e bitsoang go palo ya mekga - czworoboczny.

mefuta efe ya quads ntse a ithuta ka curriculum sekolo

Ka le geometry morao-rao tse 4 tsa mofuta dikhutlontsi ka mahlakoreng a mane. Leha ho le joalo, ka lebaka la ho thepa e rarahaneng haholo ea ho ba bang ba bona ha ba le litlelase tsa lipalo, geometry sekolong ba tseba feela ka mefuta e 'meli.

• Pharallelokeramo (pharallelokeramo). The mahlakoreng a nkhanyetsa le ho ba sekhutlonne ba tšoanang le mong ho e mong 'me, ka ho latellana, baa lekana ka bobedi.
• Trapezoid (trapezium kapa trapezoid). sekhutlonne ena e na le tse peli mahlakoreng a mabeli e tšoanang le mong ho e mong. Leha ho le joalo, banyalani ba bang ba mahlakoreng ha se na karolo e joalo.

Ha o ile a ithuta ka tsela e sekolo tsa mefuta le geometry tsa quadrangles

Ho phaella ho tsena, ho na le mefuta e 'meli ea quadrangles le eo baithuti ba sa tsebe ho lintho tseo ba le geometry, ka lebaka la ho rarahana bona e khethehileng.

• Deltoid (k'haete) - palo, moo mong le e mong lipara tse peli tsa mahlakoreng haufi lekana ka bolelele mong ho e mong. Lebitso la quadrangle ena e ne e le ka lebaka la 'nete ea hore le ponahalo a ke haholo re hopotsang ea lengolo la alfabeta Segerike - "makgobokgobo".
• Pharallelokeramo (antiparallelogram) - palo ena e ka rarahaneng e le lebitso la eona. Ka ho ba babeli ba mahlakoreng a mabeli a lekanang, empa ha ba e tšoanang le mong ho e mong. Ho feta moo, mahlakoreng telele fapaneng quadrangle le intersect ka tswelediso tse ling tse peli tse khutšoanyane mahlakoreng.

mefuta pharallelokeramo

Kaha a ileng a sebelisana le mefuta e ka sehloohong ea quads, o lokela ho lefa a lebisa tlhokomelo ho subspecies lona. Ho joalo, parallelograms tsohle, le eena, a ba boetse ba arotsoe ka lihlopha tse 'nè.

• Classic pharallelokeramo.
• Rhombus (rhombus) - quadrangular sebopeho le mahlakoreng lekanang. diagonals lona intersect ka mahlakoreng le letona, ho arola rhombus ka mane dikhutlotharo lekanang letona angled.
• Khutlonne (khutlonne). lebitso lena ipuella. Kaha khutlonne sena ka mahlakoreng le letona (mong le e mong ba lekantse le likhato mashome a robong). bo fapaneng mahlakoreng ha feela e tšoanang le mong ho e mong, empa e lekanang.
• Square (lisekoere). Ka kgutlotharong ke sekhutlonne le dikhutlo e nepahetseng, empa o na le ka mahlakoreng 'ohle lekanang. Ena, palo ena e haufi le taemane e. Gore e tle e ka pheha khang ea hore e le boholo ba lisekoere - ke sefapano pakeng tsa taemane le khutlonne.

The khethehileng thepa ya khutlonnetsepa le

Ho nahana ka litšoantšo tsa ka, eo ho eona e mong le e ba likhutlong pakeng mahlakoreng o lekana le likhato mashome a robong, e Ke habohlokoa e shebana le kamano e haufi ka kgutlotharong. Ho joalo, seo bontšang hore o na le litšobotsi tse e khetholla ho tloha parallelograms tse ling?

Ho tiisa hore taba eo pharallelokeramo - khutlonnetsepa, diagonals lona lokela ho lekana le e mong mong, 'me e mong le e ba likhutlong le - otlolohile. Ho phaella moo, boholo ba lisekoere tsa diagonals lona ba lokela ho finyella Balang ea mapatlelong a mahlakore a mabeli a bapileng ea palo eo. Ka mantsoe a mang, e khutlonne classic na le dikhutlotharo pedi letona angled, ha ba ntse ba li tsejoa, Balang ea mapatlelong a maoto ke ba lekanang le lisekoere tsa hypotenuse ena. Ka karolo e phethoang ke hypotenuse ho sebeletsa diagonale lebesisisa quadrangle.

A ho qetela a lipontšo tsena tsa palo ena hape ke thepa ea lona e khethehileng. Ho phaella moo, ho na le ba bang. Ka mohlala, ha e le hantle hore mekga tsohle ithutile quadrangle le dikhutlo e nepahetseng - ke bobeli bophahamo ba eona.

Ho feta moo, haeba le khutlonne pota mong le e atamela selika-likoe, bophara ba sona e tla ba lekanang le diagonale tsa dibopeho le ngotsoe.

Har'a thepa tse ling tsa sekhutlonne sa, taba ea hore ho a bataletse 'me batho bao e seng Euclidean thutatekanyong ha e yo. Sena ke ka ntlha ya go ha e le hantle hore tsamaisong e joalo ho na le ho na palo quadrangular, o bala dikhutloteng le o lekana le likhato tse makholo a mararo le mashome a tšeletseng.

Sekwere le litšobotsi tsa lona

Kaha ileng a sebetsana le litšobotsi le thepa ya khutlonnetsepa le, o lokela ho lefa a lebisa tlhokomelo ho bobeli tsebahalang saense e quadrangle le dikhutlo e nepahetseng (a lisekoere).

Jwalo ka ha e le hantle e khutlonne tšoanang, empa ka mahlakoreng lekana, sebopeho sena se kaofela ha thepa ea eona. Empa ho fapana le eena, le boholo ba lisekoere ke le teng ka ba le geometry bao e seng Euclidean.

Ho phaella moo, ka palo ena, ho na le tse ling tse le litšobotsi tse ka bomong. Ka mohlala, taba ea hore ho tobana ea lisekoere e hase feela e lekanang mong ho e mong, empa intersect ka mahlakoreng le letona. Kahoo, e le rhombus ka, sekoere entsoeng ka dikhutlotharo mane letona angled, eo e arotsoe diagonally.

Ho phaella moo, palo ena ke e leka-lekaneng ka ho fetisisa quadrangles tsohle.

ke chelete ea dikhutlo tsa sekhutlonne le seo

Ho nahana ka litšobotsi tsa quadrangles tsa Euclidean le geometry, o lokela ho lefa a lebisa tlhokomelo ho likhutlong tsa bona.

Kahoo, ka mong le e mong litšoantšo tsa ka holimo, ho sa natswe hore na ho dikhutloteng hae le letona kapa che, kakaretso ea bona e lula e tšoanang - likhato tse makholo a mararo le mashome a tšeletseng. Ena ke tšobotsi e ikhethang ea mofuta ona wa lipalo.

quadrangles pherimitha

Kaha a ileng a sebetsana le seo, se Balang tsa dikhutloteng tsa sekhutlonne le thepa tse ding e khethehileng ea sebopeho ea mofuta ona, e ke ho hlokahala hore ho tseba hore na ke molemo ka ho fetisisa ea ho sebelisa mekhoa ea ho a bale pherimitha bona le sebakeng seo.

Ho fumana hore na pherimitha ya sekhutlonne efe kapa efe, ho hlokahale feela eketsa ho fihlela ho e mong e mong bolelele ba mahlakore a eona.

Ka mohlala, ka sa feiga KLMN sedikiso lona ka balwa ka moralo wa: P = KL + LM + MN + kn dostupnost. Haeba re ka nkang sebaka mona linomoro fumana: 6 + 8 + 6 + 8 = 28 (cm,).

Tabeng ea moo palo nkoa - sekoere kapa rhombus, bakeng sa ho fumana ka pherimitha ya moralo wa ka ho nolofalitse ka hore feela ho ata bolelele ba e mong oa mahlakoreng a sona ka ho ba bane P: x = KL mohlala 4. 6: x 4 = 24 (cm,).

Moralo quadrangles Square

Kaha ileng a sebetsana le kamoo ho fumana pherimitha ya sebopeho leha e le efe nang le likhutlo tse 'nè le mahlakore a lokelang ho nahana ka ho fetisisa ratoa ho le bonolo tsela ea ho fumana sebakeng sa hae.

• Tsela ea khale ho a bale e - sena ke ho sebelisa moralo S = 1/2 × Ln KM x SEBE Lon. E fellang kateng le hore sebakeng seo leha e le efe ea quadrangle ke lekanang le sehlahisoa halofo ea diagonals ka sine tsa hlaha ka lehlakoreng le leng pakeng tsa bona.
• Ha palo eo sebakeng seo lokela ho fumana - e 'se khutlonnetsepa kapa lisekoere (the diagonale ea tsona e kamehla lekanang mong ho e mong), re ka nolofatsa moralo wa, emisoa ka lisekoere tsa bolelele ba diagonale mong le ata e ke sine tsa hlaha ka lehlakoreng le pakeng tsa bona le ho arola ka halofo tsohle. Mohlala: S = 1/2 CM ^2: x SEBE Lon.
• Hape, ha ho sebaka sa khutlonnetsepa e ka u thusa hore ka pherimitha nkoa lipalo e le bolelele ba e mong oa mahlakoreng a sona. Boemong bo joalo ho tla ba ho fetisisa expedient ho sebelisa moralo S = kn dostupnost: x (P - 2 kn dostupnost) / 2.
• Tabeng ea lisekoere tsa thepa tsa lona lumella tšebeliso ea mekhoa 'maloa tse eketsehileng ho fumana sebakeng seo. Mohlala, ka ho tseba dibopeho tsena pherimitha 'na ha sebelisoa fapaneng joalo: S = P ² / 16. 'Me haeba tsebahalang radius ea selika-likoe ngotsoe sekhutlonne ka, e le sebaka seo boholo ba lisekoere ke tsela haholo tšoanang: S = 4r ^2. Ha radius ea lesakaneng o tsejoa, loketse ebe tse ling moralo: S = 2R ^2. Hape, e leng sebaka le boholo ba lisekoere o lekana le 0,8 telele mola huleloa ho tswa ho sekhutlo ba palo ho bohareng ba lehlakoreng le leng.
• , Ho phaella ho ka holimo ho tsohle, ho na le boetse ho na le moralo o balletsweng arohaneng bakeng sa ho fumana sebaka seo, tse reretsoeng ho toba ho pharallelokeramo ena. Ho ka sebelisoa, ha a tsebe, bolelele ba libaka tse phahameng tse peli tsa palo eo le boholo ba hlaha ka lehlakoreng le pakeng tsa bona. Joale, bophahamo ba lokela ho ata ka mong ho e mong le sine tsa hlaha ka lehlakoreng le pakeng tsa bona. Ke habohlokoa ho hlokomela hore u ka sebelisa moralo ona ho litšoantšo tsohle, eo e amana parallelograms le (khr, khutlonne, rhombus le lisekoere).

Tse ling tse thepa quadrangles: didikadikwe ngotsoe le maemo ho

Kaha ba nka litšobotsi le thepa ya quadrangle e le sebōpeho sa Euclidean le geometry, ho ke ke bohlokoa ho ela hloko le monyetla ho hlalosa ho potoloha kapa kena ka hare ho latelang:

• Ha chelete ea dikhutloteng se fapaneng le mokhabo nyoloha ka likhato tse lekholo le mashome a robeli 'me baa lekana mong ho e mong, ho ka etsahala ho hlalosa lesakaneng le ka bolokolohi ho pota quadrangle ena.
• Ho latela Theorem Ptolemy e, haeba tse hlalositsoeng lesakaneng le ka ntle ho khutlontsi ka mahlakoreng a mane, sehlahisoa sa diagonals ho lekana chelete eo ea lihlahisoa tsa mahlakoreng a mabeli ba palo eo. Kahoo, moralo e ne e tla ba e reng: CM: x Ln = KL x, MN + LM: x kn dostupnost.
• Haeba u haha khutlonne oo chelete ea mahlakoreng a mabeli li lekana le e mong mong, ka nako eo ho ke ke ho bonolo ho inscribe selika-likoe.

Kaha a ileng a sebetsana le taba ea hore e joalo e sekhutlonne eo mefuta eohle ea e-ba teng, e leng batho ba nang le dikhutlo e nepahetseng feela pakeng tsa mekga e le hore thepa ba nang le sona, ba lokela ho hopola sepakbola ena kaofela. Ka moralo ho khetheha ho fumana pherimitha le sebakeng dikhutlontsi ho nahana ka tsona. Ka mor'a hore tsohle, palo ea foromo ena - e mong oa atileng ka ho fetisisa, 'me tsebo ena e ka ba molemo bakeng sa ho dipalelo ka bophelo ba sebele.