Quadrangle ne engile - yinto lodibaniso eliyi Ikwadrilatherali ...

Enye izihloko ezininzi ezinomdla kakhulu geometry konyaka wesikolo - yi "Ikwadrilatherali" (Grade 8). Ziziphi iintlobo manani ezikhoyo, yintoni iimpawu ezikhethekileyo ezinawo? Yintoni le yayahlukile quadrangles kunye engile degrees asithoba na? Makhe sijonge konke oku.

Ingaba zejometri ebizwa quadrangle

Eneepoligoni ezinama macala omane, ngokulandelelana, le eziphezulu amane (iikona) nokubizwa quadrangles geometry Euclidean.

Unomdla kwimbali olu hlobo yamanani yegama. Ngolwimi Russian isibizo "Ikwadrilatherali" livela kwi "ezine iikona" amabinzana (ngendlela enye njenge "unxantathu" - i-engile amathathu, "pentagon" - engile ezintlanu, njl ...).

Noko ke, ngo-Latin (owabakhoyo ngenxa yolamlo amagama amaninzi zejiyometri ngeelwimi ezininzi zehlabathi) ibizwa ngokuba Ikwadrilatherali. Eli gama i Quadri yesi (emine) kunye latus noun (ecaleni). Ukuze sikwazi ukubona ukuba lo wamandulo le polygon yayisaziwa kuphela "Ikwadrilatherali".

Hi ndlela leyi, igama (ekuye kwagxininiswa ubukho engumfuziselo olu hlobo kumacala omane, hayi iikona) igcinwe kwezinye iilwimi namhlanje. Hi xikombiso, ku IsiNgesi - Ikwadrilatherali kwaye isiFrentshi - quadrilatère.

Ezininzi iilwimi Slavic olu hlobo kuchongwa amanani nangoku kwinani ezimbombeni, hayi emacaleni. Umzekelo, kwi-Slovak (štvoruholník), kwi-Bulgarian ( 'chetiriglnik ") e Belarus (" chatyrohkutnіk ") e Ukrainian (" chotirikutnik "), in Czech (čtyřúhelník), kodwa quadrangle Polish wanqula inani amaqela - czworoboczny.

Ziziphi iindidi quads efundwayo kwikharityhulam yesikolo

Geometry mihla iintlobo-4 yeepolygons kunye macala omane. Nangona kunjalo, ngenxa iimpawu entsonkothileyo kakhulu abanye babo kwiiklasi geometry zesikolo eziqhelekileyo kuphela iintlobo ezimbini.

• Parallelogram (parallelogram). Amacala ababephikisana Ikwadrilatherali zezi parallel omnye komnye yaye, ngokulandelelana, bayalingana ngababini.
• Trapezoid (kwikasi okanye trapezoid). Le Ikwadrilatherali iqulathe macala mabini malunga kuhambisana omnye komnye. Noko ke, enye iperi emacaleni akanayo enjalo.

Fundanga kwi zifundo lweentlobo geometry we quadrangles

Ukongeza kwezi, kukho iindidi ezimbini quadrangles ngalo abafundi bengakuthandi eziqhelekileyo izifundo geometry, ngenxa yokuntsonkotha zabo ezizodwa.

• Deltoid (yephepha) - nani, apho nganye ngambini macala ezikufutshane elilinganayo ubude omnye komnye. Igama le quadrangle ngenxa yokuba ngembonakalo nguye kakhulu embhoxo unobumba we-alfabhethi Greek - "delta".
• Parallelogram (antiparallelogram) - eli nani nje ezintsonkothileyo negama layo. Kulo macala mabini esahlukileyo bayalingana, kodwa azikho zifana omnye komnye. Ngaphezu koko, emacaleni elide icala quadrangle phambana njengoko phambili nezinye macala mabini mfutshane.

iintlobo parallelogram

Kokuba kusetyenzwe iintlobo eziphambili quads, kufuneka sinikele ingqalelo ohlobo yayo. Ngoko ke, zonke parallelograms, ke, nazo yahlulwe kumaqela amane.

• parallelogram Classic.
• Irhombus (irhombus) - imilo quadrangular enamacala alinganayo. idayagonali yayo yabanikazi kwi engile, ukulaba irhombus ibe oonxantathu ezine ekunene-engile egqithe elilinganayo.
• Uxande (uxande). Eli gama lithetha ukuba ngokwayo. Ekubeni le Uxande engile (ngamnye kubo ulingana degrees alithoba). ngapha nangapha kuphela zifana omnye komnye, kodwa ngokulinganayo.
• Square (square). Njengoko Uxande kukho Ikwadrilatherali kunye engile ekunene, kodwa yena uye macala onke alinganayo. Oku, eli nani asondele nekalikedo. Ngoko ke Kungaphikiswa ukuba isikwere - yinto umnqamlezo phakathi diamond kunye uxande.

Iimpawu ezikhethekileyo elide

Ujonge amanani, apho nganye emasondweni phakathi amacala ulingana degrees asithoba, kubalulekile ukuba kugxininiswe ngakumbi phezu uxande. Ngoko ke, yintoni iimpawu ukuba uneempawu ezahlula kwezinye parallelograms?

Babonisa ukuba parallelogram sifundo - uxande, idayagonali zayo kufuneka ilingane omnye komnye, yaye ngamnye ezimbombeni - tye. Ukongeza, isikweri idayagonali zayo kufuneka ihlangabezane udibaniso lwezikweri wamacala amabini osecaleni lo mzobo. Ngamanye amazwi, le uxande classical ibandakanya triangles ezimbini ekunene kwelinye icala ngesiquphe, njengoko baziwa, udibaniso lwezikweri imilenze lilingana isikweri hypotenuse. Xa indima hypotenuse ikhonza quadrangle oxwesileyo ngazo.

Owokugqibela le miqondiso lo mzobo kwakhona impahla yalo ekhethekileyo. Ukongeza, kukho abanye. Ngokomzekelo, into yokuba onke amaqela wafunda quadrangle kunye engile - na ukuphakama kwalo zombini.

Ngaphezu koko, ukuba uxande macala nganye bazobe isangqa, ububanzi bayo iya kulingana ukuya idiagonal milo sibhalwe.

Phakathi kwezinye iimpawu Ikwadrilatherali, isibakala ukuba tyaba kwaye non-Euclidean geometry ayikho. Oku kungenxa yokuba kule nkqubo akukho nani quadrangular, udibaniso engile ulingana degrees ezimakhulu mathathu anamanci mathandathu.

Isikwere kunye neempawu zayo

Kokuba kusetyenzwe iimpawu kunye neempawu uxande, kufuneka sinikele ingqalelo quadrangle inzululwazi eyaziwa yesibini engile (a isikwere).

Njengoko enyanisweni uxande efanayo, kodwa amacala alingane, le imilo zonke iipropati yayo. Kodwa ngokungafaniyo kuye, isikwere ekhoyo kwi geometry non-Euclidean.

Ukongeza, kweli nani, kukho ezinye iimpawu ngamnye. Umzekelo, isibakala sokuba idiagonal wesikwere ayikho nje ilingana omnye komnye, kodwa phambana kwi engile. Ngenxa yoko, njengokuba irhombus, isikwere eliquka oonxantathu ezine ekunene-engile egqithe, leyo yahlulwe kwikonw ngekona.

Ukongeza, eli nani yeyona elungeleleneyo zonke quadrangles.

Yintoni udibaniso eliyi Ikwadrilatherali

Ukuqwalasela iimpawu quadrangles ka Euclidean geometry, kufuneka sinikele ingqalelo iikona zabo.

Ngenxa yoko, xa ngamnye kuloo manani angentla, kungakhathaliseki nokuba kukho kuwo engile sabo sokunene okanye hayi, imali iyonke kubo sisoloko efanayo - izidanga ezimakhulu mathathu anamanci mathandathu. Lo ngumsebenzi eyodwa olu hlobo amanani.

quadrangles lokubiyela

Akuba awaqhubana ngayo koko, yintoni na umdibaniso eliyi Ikwadrilatherali kunye nezinye iimpawu ezikhethekileyo imilo yolu hlobo, kuyimfuneko ukuba bayayazi into ofanele ukusebenzisa ifomula ukubala iperimitha yabo ndawo.

Ukuze ubone kujikelezo nayiphi Ikwadrilatherali, nimelwe dibanisa kuphela omnye komnye ubude macala omabini.

Hi xikombiso, ku Isazobe KLMN umtya bayo bangonakala ibalwa wokubala: P = kl + LM + MN + KN. Ukuba we shintsha apha amanani afunyenwe: 6 + 8 + 6 + 8 = 28 (cm).

Kwimeko apho lomzobo ingqalelo - isikwere okanye irhombus, ngokuba ekufumaneni kujikelezo kwifomula kube lula ngokuthi phinda nje ubude elinye macala zayo P ezine x = kl umzekelo 4. 6 x 4 = 24 (cm).

Formula quadrangles Square

Ekubeni kujongana ukufumana indlela kujikelezo nayiphi na imilo ezimbombeni zone kunye namacala kufuneka iqwalasele le ndlela ithandwa kakhulu kwaye kulula kakhulu ukufumana indawo yakhe.

• Indlela classic ukubala ngayo - oku ukusebenzisa i S ifomula = 1/2 × LN KM x SIN Lon. Kubonakala ukuba nayiphi na indawo ye quadrangle uyalingana isiqingatha imveliso ye idayagonali kwi i sine ye-engile phakathi kwabo.
• Ukuba lo mzobo wendawo kufuneka ukufumana - oko uxande okanye isikwere (i idiagonal apho usoloko ulingana omnye komnye), singakwazi lula ifomula, eyakhiwa isikweri ubude enye oxwesileyo, anandise kuyo i sine ye-engile ephakathi kwabo ezisahlulayo isiqingatha zonke. Umzekelo: S = 1/2 CM ² x SIN Lon.
• Kwakhona, xa indawo uxande kunokunceda malunga amanani umjikelezo ingqalelo kwaye ubude elinye macala. Kwimeko enjalo uya kuba kufanelekile kakhulu ukuba ukusebenzisa i S ifomula = KN x (P - 2 KN) / 2.
• Kwimeko kwisikweri lweepropati yayo ukuvumela ukusetyenziswa iifomyula eziliqela ezongezelelweyo ukufumana indawo. Ngokomzekelo, ukwazi iimilo iperimitha enokusetyenziswa lobeko loo: S = P ^2/16 Ke ukuba radius eyaziwa wesangqa abhaliwe Ikwadrilatherali, indawo square yindlela efanayo kakhulu: S = 4r ^2. Ukuba radius wesangqa yaziwa, ngoko enye indlela efanelekileyo: S = 2R ^2. Kwakhona, indawo square ilingana 0.8 avela kwikona inani ukuya kumbindi icala umgca elide.
• Ukongeza zonke ngasentla, kukho kwakhona indlela eyahlukileyo ngokufumana le ndawo, eyenzelwe ngokukodwa parallelogram. kokuba usetyenziswe, ukuba uyaziwa, nobude eziphakamileyo ezimbini mzobo kunye nobungakanani engile ephakathi kwabo. Emva koko, ukuphakama Wandisa omnye nomnye kunye sine ye-engile ephakathi kwabo. Kubalulekile ukuphawula ukuba ungasebenzisa le formula onke amanani, leyo enxulumene parallelograms (oko kukuthi, uxande, irhombus kunye square).

Ezinye iimpawu quadrangles: izangqa sibhalwe kwaye nezisekelwe

Ekubeni ingqalelo iimpawu kunye neempawu a quadrangle njengoko imilo Euclidean geometry, kubalulekile ukunikela ingqalelo ithuba ukuchaza umjikelo okanye angene ngaphakathi kulandelayo:

• Ukuba udibaniso engile malunga ye isafobe ngomoya izidanga elikhulu elinamanci asibhozo kwaye lingana omnye komnye, unako ukuchaza isangqa ngokukhululekileyo kule quadrangle.
• Ngokutsho theorem lukaPtolemy, ukuba kwesangqa ochazwe ngaphandle polygon kunye kumacala omane, imveliso ye idayagonali ilingana udibaniso iimveliso kumacala ahlukeneyo mzobo. Ngenxa yoko, ifomula bekuya kuba: CM x LN = kl x MN + LM x KN.
• Ukuba ukwakha uxande apho sum of kwicala elijongene ayalingana omnye komnye, ngoko kusenokwenzeka ukuba sizibhale isangqa.

Ukuba iyitshinizele nesibakala sokuba Ikwadrilatherali enjalo apho zikhona iintlobo nto, nto kufuneka engile kuphela ekunene phakathi kwamaqela kunye iimpawu abanazo, kufuneka uyikhumbule yonke le nto. Xa ifomula ethile ekufumaneni iperimitha kunye ummandla iimilo ingqalelo. Ngapha koko, eli nani le fomu - enye ixhaphakileyo, yaye olu lwazi kunokuba luncedo izibalo ebomini.