Quadrangle ndi kumathandiza kupeza ngodya zabwino bwino - ndi Uwerenge kumathandiza kupeza ngodya zabwino za quadrilateral ndi ...

Mmodzi wa mitu chidwi kwambiri mu Masamu chaka sukulu - ndi "quadrilateral ndi" (kalasi 8). Kodi mitundu ya kanjedza kulibe, chimene wapadera makhalidwe ali nazo? Kodi wapadera quadrangles ndi kumathandiza kupeza ngodya zabwino madigiri nainte? Tiyeni tione zonsezi.

Kodi geometrical chithunzi wotchedwa quadrangle

Polygons kuti zigwirizana mbali zinayi, motero, mwa mfundo zinayi (ngodya) ankadziwikanso quadrangles Euclidean Masamu.

Chidwi ndi mbiri ya mtundu wa kanjedza dzina. Chinenero cha Chirasha ndi nauni "quadrilateral" lachokera ku "ngodya zinai" mawu (chimodzimodzi monga "makona" - pa kumathandiza kupeza ngodya zitatu, "Pentagon" - kumathandiza kupeza ngodya zabwino asanu, etc ...).

Komabe, mu Latin (amene adadza mwa kuyimira a mawu ambiri zojambula mu zinenero zambiri za dziko lapansi) iwo akutchedwa quadrilateral. Liwu ili ndi numeral Quadri (anayi) ndi latus nauni (mbali). Choncho tinganene kuti wakale polygon imeneyi anadziwika kokha ngati "quadrilateral".

Mwa njira, dzina (ndi motsindika pamaso pa zithunzi za mtundu uwu wa mbali zinayi, osati ngodya) anapitiriza m'zilankhulo zina zamakono. Mwachitsanzo, mu English - quadrilateral ndi French - quadrilatère.

M'zinenero zambiri Asilavo mitundu imafotokozedwa kanjedza akadali pa chiwerengero cha ngodya, osati mbali. Mwachitsanzo, mu Slovak (štvoruholník), mu Chibugariya ( 'chetiriglnik ") mu Belarus (" chatyrohkutnіk ") mu Chiyukireniya (" chotirikutnik "), mu Czech (čtyřúhelník), koma mu quadrangle Polish otchedwa chiwerengero cha zipani - czworoboczny.

Kodi ndi mitundu iti ya quads akuphunziridwa mu maphunziro a kusukulu

Mu Masamu masiku ano 4 yonse ya polygons ndi mbali zinayi. Komabe, chifukwa katundu zovuta ena a iwo pa makalasi Masamu sukulu amadziwa yekha ndi mitundu iwiri.

• Parallelogram (parallelogram). Mbali wotsutsana wa quadrilateral ndi kufanana kwa wina ndi mzake, motero, ndi ofanana awiriawiri.
• Trapezoid (trapezium kapena trapezoid). quadrilateral tichipeza awiri zomenyanazo ikufanana ndi mzake. Komabe, awiri ena a mbali alibe Mbali zimenezi.

Sanapite ku Maphunziro a mitundu Masamu quadrangles

Kuwonjezera izi, pali mitundu iwiri ya quadrangles ndi zomwe ophunzira si bwino kuti maphunziro a masamu, chifukwa cha kapangidwe zawo zapadela.

• Deltoid (mphamba) - chithunzi, mmene aliyense wa awiriawiri awiri a m'mbali pafupi zofanana kutalika kwa wina ndi mzake. Dzina la quadrangle ichi chinali chifukwa chakuti anali wooneka ali ndithu amatikumbutsa lemba la zilembo Greek - "ankadziwana".
• Parallelogram (antiparallelogram) - chithunzi ichi ndi zovuta dzina lake. Mmenemo awiri zomenyanazo ofanana, koma sikuti ikufanana ndi mzake. Komanso, mbali yaitali wosiyana quadrangle ndi intersect monga kupitiriza ena awiri wamfupi mbali.

mitundu ya parallelogram

Popeza anachitira mitundu ikuluikulu ya quads, muyenera kulabadira subspecies ake. Choncho, parallelograms onse, amapatsidwa anagawa m'magulu anayi.

• Classic parallelogram.
• Rhombus (rhombus) - quadrangular mawonekedwe ndi mbali ofanana. diagonals ake intersect pa kumathandiza kupeza ngodya zabwino bwino, kugawa rhombus mu zinayi Triangles ofanana bwino-angled.
• Rectangle (rectangle). Dzina limeneli odziwikiratu. Popeza rectangle ndi kumathandiza kupeza ngodya zabwino bwino (yense wa iwo wofanana madigiri nainte). moyang'anizana mbali osati ikufanana ndi mzake, koma ofanana.
• Square (lalikulu). Monga rectangle ndi quadrilateral ndi kumathandiza kupeza ngodya zabwino, koma iye ali kumbali zonse zofanana. Ichi, chithunzi ichi uli pafupi ndi mwala. Tingathe amanena kuti lalikulu - ndi mtanda pakati daimondi ndi rectangle.

The wapadera katundu wa rectangle ndi

Poganizira kanjedza, imene aliyense ngodya pakati pa mbali ndi wofanana ndi madigiri makumi asanu ndi anayi, tiyenera zofunika pafupi pa rectangle lapansi. Choncho, zimene zimaonetsa kuti ali ndi makhalidwe amene kuwasiyanitsa ndi parallelograms ena?

Kunena kuti nkhani parallelogram - ndi rectangle, diagonals ake ayenera kukhala wolingana ndi munthu wina ndipo aliyense wa ngodya - molunjika. Komanso, m'bwalo la diagonals ake ayenera kukumana Uwerenge mabwalo mbali ziwiri moyandikana wa maonekedwe. Mu mawu ena, rectangle chakale tichipeza Triangles awiri kudzanja angled, monga amadziwika, Uwerenge mabwalo miyendo ndi wofanana ndi m'bwalo la hypotenuse lapansi. Paudindo hypotenuse ndi akutumikira opendekera ankaona quadrangle.

Otsiriza a zizindikiro chithunzi Izinso katundu yache. Komanso pali ena. Mwachitsanzo, popeza kuti magulu onse anaphunzira quadrangle ndi kumathandiza kupeza ngodya zabwino bwino - ndi msinkhu wake.

Komanso, ngati rectangle iliyonse jambulani chozungulira china, m'mimba ake adzakhala wofanana ndi opendekera mosiyanasiyana ndi alembedwa.

Mwa zina za quadrilateral ndi, popeza kuti pangotsala ndipo sanali Euclidean Masamu kulibe. Ichi ndi chifukwa chakuti mu dongosolo palibe chithunzi quadrangular, Uwerenge kumathandiza kupeza ngodya zabwino ndi wofanana ndi madigiri mazana atatu ndi makumi asanu.

Lalikulu ndi zochititsa

Popeza anachita nawo maonekedwe komanso katundu wa rectangle, muyenera khutu ku chachiwiri kudziwika sayansi quadrangle ndi kumathandiza kupeza ngodya zabwino bwino (a lalikulu).

Monga mu choona rectangle chomwecho, koma ndi mbali ofanana, mawonekedwe uyu ali onse katundu wake. Koma mosiyana ndi iye, lalikulu alipo mu Masamu sanali Euclidean.

Komanso, mu chithunzi ichi, pali ena makhalidwe payekha. Mwachitsanzo, mfundo kuti opendekera a lalikulu si chabe wofanana ndi mzake, koma intersect pa kumathandiza kupeza ngodya zabwino bwino. Choncho, ngati rhombus, ndi lalikulu ongokhala Triangles anayi bwino-angled, amene amakhala wogawanika diagonally.

Komanso, chithunzi ichi ndi moyenera ambiri quadrangles onse.

ndi Uwerenge kumathandiza kupeza ngodya zabwino za quadrilateral chimene

Poganizira maonekedwe a quadrangles wa Euclidean Masamu, muyenera khutu ku ngodya zawo.

Choncho, aliyense wa kanjedza pamwamba, osayang'ana ngati mwa kumathandiza kupeza ngodya zabwino lake lamanja kapena ayi, chiwerengero cha iwo yofanana - madigiri mazana atatu ndi makumi asanu. Iyi ndi mbali yapadera mtundu wa kanjedza.

quadrangles wozungulira

Popeza anachitira ndi kuti, kodi Uwerenge kumathandiza kupeza ngodya zabwino kwa quadrilateral ndi katundu wina wapadera wa mawonekedwe a mtundu umenewu, m'pofunika kudziwa bwino ntchito mitunduyi kuwerengera wozungulira awo ndi madera.

Kudziwa kukafika kutsogolo kwa quadrilateral aliyense, Tiyenera kuwonjezera kwa wina ndi mzake kutalika kwa mbali zonse.

Mwachitsanzo, mu mkuyu KLMN circumference ake kuchita masamu mfundo: P = KL + LM + MN + KN. Ngati ife mmalo pano manambala analandira: 6 + 8 + 6 + 8 = 28 (cm).

Ngati kumene chithunzi ankaona - apakati kapena rhombus, kupeza kukafika kutsogolo kwa chilinganizo akhoza wosalira basi kuchulukitsa kutalika kwa mmodzi wa m'mbali mwake ndi anayi P × = KL Mwachitsanzo 4. 6 × 4 = 24 (cm).

Chilinganizo quadrangles Square

Popeza anachitira ndi mmene kupeza kukafika kutsogolo kwa mawonekedwe aliyense ndi ngodya zinai ndi mbali tiyenera kuganizira wotchuka kwambiri ndi zophweka kupeza malo ake.

• Njira yakale kuwerengera izo - izi ndi kugwiritsa ntchito mfundo S = 1/2 × Ln Km X TCHIMO Lon. Iwo likukhalira kuti zosiyanasiyana quadrangle ndi wofanana ndi mankhwala theka la diagonals pa sine ya njingayo unali pakati pa iwo.
• Ngati chithunzi amene m'dera ayenera kupeza - ndi rectangle kapena lalikulu (a opendekera amene nthawi zonse wofanana mzake), tikhoza wosalira njira anamangidwa m'bwalo la kutalika kwa opendekera wina ndi kuchulukitsa izo mwa sine ya njingayo pakati pa iwo ndi kugawa mu theka zonse. Mwachitsanzo: S = 1/2 masentimita ² × TCHIMO Lon.
• Komanso, pamene m'dera la rectangle kungathandize bwanji wozungulira ankaona kanjedza ndi kutalika kwa mmodzi wa m'mbali mwake. Zikatero zidzakhala kwambiri kuyenera ntchito chilinganizo S = KN × (P - 2 KN) / 2.
• Pankhani ya m'bwalo la katundu kulola kugwiritsa ntchito Njira zingapo zina kupeza m'deralo. Mwachitsanzo, podziwa akalumikidzidwa wozungulira angagwiritsidwe ntchito zosinthika amenewa: S = P ² / 16. Ndipo ngati kudziwika utali wozungulira bwalo alembedwa quadrilateral ndi, dera lalikulu ndi njira kwambiri ofanana: S = 4r ^2. Ngati utali wozungulira bwalo amadziwika, oyenera ndiye zina chilinganizo: S = 2R ^2. Komanso, dera lalikulu ndi wofanana 0,8 yaitali mzere limachokera ku ngodya ya chithunzi pakati pa mbali ina.
• Kuwonjezera pa pamwamba pa zonse, palinso chilinganizo osiyana kupeza m'dera, apangidwa makamaka kuti parallelogram lapansi. Thiabendazole angagwiritsidwe ntchito, ngati amadziwika, kutalika kwa misanje awiri chithunzi ndi kukula kwa mbali pakati pawo. Ndiye, kutalika kwa kuchulukitsa ndi mzake ndi sine ya njingayo pakati pawo. Dziwani kuti mungathe kugwiritsa ntchito dongosolo ili ndi lipoti onse, amene ikukhudzana bwanji ndi parallelograms ndi (ie, rectangle, rhombus ndi lalikulu).

Other katundu quadrangles: mabwalo lolembedwa ndi circumscribed

Popeza kuti takambilana makhalidwe ndi katundu wa quadrangle monga mawonekedwe a Euclidean Masamu, tiyenera powasamalira n'zotheka kufotokoza wozungulira kapena kulowa mkati zotsatirazi:

• Ngati Uwerenge kumathandiza kupeza ngodya zabwino zosiyana ndi chithunzi ndi madigiri zana ndi makumi asanu ndi atatu ndi ofanana wina ndi mnzake, n'zotheka kufotokoza bwalo momasuka kuzungulira quadrangle izi.
• Malinga ndi Lingaliro Lovomerezeka Ptolemy, ngati anafotokoza bwalo kunja polygon ndi mbali zinayi, mankhwala a diagonals ndi wofanana Uwerenge mankhwala a zomenyanazo wa maonekedwe. Choncho, njira zingakhale: masentimita × Ln = KL × MN + LM × KN.
• Ukamanga rectangle imene Uwerenge zomenyanazo ali wofanana ndi munthu wina, ndiye n'zotheka kukhomereza bwalo.

Popeza anachitira ndi mfundo zimenezi quadrilateral amene yonse ya iyo kulibe, amene ali kumathandiza kupeza ngodya zabwino bwino pakati pa zipani ndi zomwe katundu ali, ayenera kukumbukira zinthu zonse izi. Dongosolo makamaka kupeza wozungulira ndi dera polygons wa nkhani. Ndipotu chithunzi cha fomu iyi - mmodzi wa ambiri, ndipo kudziwa zimenezi kungakhale kothandiza kwa anapezazo mu moyo weniweniwo.