Quadrangle rworudyi pamakona - ari vakaverenga pamakona ane quadrilateral ...

Imwe zvinofadza zvikuru misoro muna geometry kwegore - ndi "quadrilateral" (Grade 8). Ndezvipi arimowo, chii chinokosha unhu nhaka? Chii chakasiyana quadrangles vane pamakona ose mapfumbamwe madhigirii? Ngatimboonai izvi zvose.

Chii geometrical mufananidzo rinonzi quadrangle

Polygons kuti ine mativi mana, ukuwo, ari vertices mana (makona) vanonzi Euclidean geometry quadrangles.

Vanofarira nhoroondo iri mhando zita nemifananidzo. In mutauro wokuRussia iri rokuti "quadrilateral" rinobva "mana" Mashoko (zvakafanana sezvo "Triangle" - pamakona matatu, "nePentagon" - pamakona shanu, etc ...).

Zvisinei, muna Latin (rakasvika kubudikidza Mediation vakawanda geometric mashoko mumitauro yakawanda munyika) nayo inonzi quadrilateral. Shoko iri ndiro nhamba Quadri (mana) uye pazita latus (divi). Saka tinogona kugumisa kuti rekare polygon ichi aizivikanwa chete se "quadrilateral".

Nenzira, zita (ane kumikidzo pamberi kwokufananidzira kumativi mana, kwete pamakona mhando iyi) zvabatwa mune mimwe mitauro ano. Somuenzaniso, muna Chirungu - quadrilateral uye muna French - quadrilatère.

Mumitauro yakawanda necheSalvic mhando ichi chinozivikanwa inofananidza vachiri nhamba makona, kwete kumativi. Somuenzaniso, muna Slovak (štvoruholník), muna Bulgarian ( 'chetiriglnik ") mu Belarus (" chatyrohkutnіk ") mu wokuUkraine (" chotirikutnik "), mu Czech (čtyřúhelník), asi mukati Polish quadrangle akadana nhamba yavose - czworoboczny.

Api quads kuitwa akadzidza pachikoro hweutungamiri

In geometry ano vari 4 siyana polygons mativi mana. Zvisinei, nokuda kwazvo kunzwisisa ehupfumi vamwe vavo pamusoro chikoro geometry makirasi vari chete vanoziva mhando mbiri.

• Parallelogram (parallelogram). The kumushora kumativi quadrilateral zvinofanana kune mumwe nomumwe uye ukuwo, vakaenzana vari vaviri vaviri.
• Trapezoid (trapezium kana trapezoid). quadrilateral ichi chine akatarisana mativi maviri noku mumwe. Zvisinei, vamwe vachipiwa kumativi hakuna zvakadaro chinhu.

Not akadzidza paboka pachikoro geometry marudzi quadrangles

Kuwedzera kune izvi, pane mhando mbiri quadrangles nako vadzidzi havasi zvaizivikanwa geometry zvidzidzo, nokuda kwavo chaiyo kunzwisisa.

• Deltoid (nenjerere) - nechipi, sezvamakaropafadzwa nechimwe maviri maviri pedyo mativi akaenzana pakureba kune mumwe. Zita quadrangle uyu nokuti kuti chitarisiko ndiye zvikuru nowenyika tsamba Greek arufabheti - "Delta".
• Parallelogram (antiparallelogram) - mufananidzo uyu sezvo zvakaoma sezvo zita rayo. Mariri maviri akatarirana mativi vakaenzana, asi havana noku nepedyo. Uyezve, refu pakatarisana mativi quadrangle piringisha sezvo kuenderera mamwe mapfupi mativi maviri.

mhando parallelogram

Wakabata pamwe huru mhando quads, unofanira kuteerera subspecies ayo. Saka, parallelograms zvose, akavapindurawo, vari mapoka mapoka mana.

• Classic parallelogram.
• Rhombus (rhombus) - quadrangular chimiro zvakaenzana mativi. diagonals Its piringisha kurudyi pamakona, unonyatsoruramisa rhombus mana akaenzana zvokuridza kodzero-angled.
• Rectangle (rectangle). Zita iri anotaura pacharo. Sezvo rectangle uyu pamakona zvakanaka (nomumwe wavo zvakaenzana mapfumbamwe madhigirii). kumativi akasiyana kwete chete noku mumwe, asi vakaenzana.
• Square (Square). Sezvo rectangle ari quadrilateral rworudyi pamakona, asi ane mativi ose anoenzanirana. Izvi, nhamba iri pedyo nedhaimani. Saka unogona angapokana kuti pachivara - ndiwo muchinjikwa pakati nedhaimani uye rectangle.

The dzinokosha ehupfumi ari rectangle

Uchifunga mifananidzo, iyo mumwe nomumwe makona pakati mativi akaenzana makumi mapfumbamwe madhigirii, zvinokosha kuva pedyo chikuru pamusoro rectangle. Saka, chii inobudisa ine unhu kuti kusiyanisa kubva mamwe parallelograms?

Kutaura kuti nyaya parallelogram - a rectangle, diagonals ayo anofanira akaenzana mumwe, uye mumwe nomumwe pamakona - twasu. Mukuwedzera, mativi ose diagonals ayo anofanira kusangana Verenga dzinoungana vaviri pedyo mativi nhamba. Nemamwe mashoko, dzekare rectangle rine zvokuridza zviviri zvakanaka-angled, sezvo vanozivikanwa, vakaverenga dzinoungana vanhu makumbo akaenzana yaiungana yacho hypotenuse. In basa hypotenuse inoshanda diagonal vaiona quadrangle.

Wokupedzisira izvi zviratidzo mufananidzo uyu zvaro chaiyo. Uyezve, pane vamwe. Somuenzaniso, chokwadi kuti zvose mapato akadzidza quadrangle rworudyi pamakona - zvose kukwirira kwayo.

Uyezve, kana munhu rectangle kumativi nomumwe kudhirowa denderedzwa, ayo dhayamita achava akaenzana diagonal yacho yakanyorwa zvitarisiko.

Pakati pezvimwe zvivako zviri quadrilateral, chokwadi kuti sandara uye vasiri Euclidean geometry haako. Izvi imhaka yokuti munyika yakadaro hurongwa hapana quadrangular mufananidzo, Verengai pamakona akaenzana mazana matatu namakumi matanhatu madhigirii.

Pachivara uye mamiriro ayo

Wakabata pamwechete unhu uye zvivako zviri rectangle, unofanira kuteerera wechipiri anozivikanwa sayenzi quadrangle pamwe pamakona zvakanaka (a sikweya).

Sezvo chokwadi chete rectangle, asi zvakaenzana mativi, chimiro ichi ane ose zvivako zvayo. Asi kusiyana naye, pachivara aripo mune dzisiri Euclidean geometry.

Mukuwedzera, mumufananidzo uyu, pane zvimwe mumwe maitiro. Somuenzaniso, chokwadi chokuti diagonal ane mativi hazvingorevi kuenzana mumwe, asi piringisha kurudyi pamakona. Saka, somunhu rhombus, mumwe sikweya zvinosanganisira kodzero-angled zvokuridza mana rakakamurwa Tsanga yacho yaichekwa.

Uyezve, mufananidzo uyu kupfuura mwero dzose quadrangles.

Chii vakaverenga pamakona ane quadrilateral

Uchifunga zviri quadrangles ose Euclidean geometry, unofanira kuteerera pamakona avo.

Saka, mumwe nomumwe ari pamusoro mifananidzo, pasinei pangava ari pamakona yake kurudyi kana kwete, yaipedzerwa kwavari nguva dzose chete - mazana matatu namakumi matanhatu madhigirii. Ichi rakasiyana kuchiitwa ichi mhando nenhamba.

mukomberedzo quadrangles

Wakabata pamwechete kuti, chii vakaverenga pamakona ane quadrilateral nezvimwe inokosha zvivako zviri chimiro ichi mhando, zvinokosha kuziva chii zvakanakisisa kushandisa Masvomhu kuverenga mukomberedzo dzavo uye nharaunda.

Kuziva mukomberedzo upi quadrilateral, zvichifanira chete wedzera kusvika rimwe pakureba kumativi acho.

Somuenzaniso, muna muonde KLMN sekamufarenzi wayo anogona dzaona kubudikidza nzira: P = KL + LM + MN + KN. Kana isu kuisa pano nhamba vakawana: 6 + 8 + 6 + 8 = 28 (cm).

In Kana apo vaiona mufananidzo - a sikweya kana rhombus, nokuti kuwana mukomberedzo iri nzira inogona nyore nokungonyepedzera vachiwedzera pakureba rimwe kumativi ayo mana P x = KL muenzaniso 4. 6 X 4 = 24 (cm).

Fomura quadrangles Square

Wakabata pamwe sei kuwana mukomberedzo upi chimiro ne makona mana uye mativi vanofanira kufunga zvikuru nevanhu uye nyore nzira yokuwana nzvimbo yake.

• The klassiske nzira kuverenga nayo - ndiko kushandisa nzira S = 1/2 × LN KM x CHIVI Lon. Zvakaratidza kuti chero nzvimbo quadrangle akaenzana hafu zvibereko diagonals pamusoro Sine pakati rekona rakamiswa pakati pavo.
• Kana nhamba ane nzvimbo vanofanira kuwana - chinhu rectangle kana sikweya (the diagonal izvo anogara kuenzana mumwe), tinogona nyore kuti nzira, yakavakwa muchivara pakati pakureba imwe diagonal nokuwanza parutivi Sine iri pakona pakati pavo uye kugovera hafu zvose. Somuenzaniso: S = 1/2 CM ² X CHIVI Lon.
• Uyewo, kana nzvimbo imwe rectangle kunogona kubatsira pamusoro mukomberedzo vaiona manhamba uye urefu rimwe kumativi acho. Pakadaro zvichava zvikuru nyore kushandisa nzira S = KN X (P - 2 KN) / 2.
• Kana ari mativi ose zvivako zvayo kubvumira kushandisa dzimwe Masvomhu akawanda kuwana nzvimbo. Somuenzaniso, kuziva mukomberedzo zvitarisiko angashandiswa musiyano wezvinyorwa kwakadaro: S = P ² / 16. Kana anozivikanwa nharaunda yacho yakanyorwa denderedzwa iri quadrilateral, sikweya nzvimbo iri zvikuru Saizvozvowo: S = 4r ^2. Kana nharaunda yacho denderedzwa chikazozikamwa, zvino vamwe zvakakodzera payakavakirwa: S = 2R ^2. Uyewo, sikweya nzvimbo akaenzana 0,8 mutsetse refu kubva pakona mufananidzo kusvikira pakati rumwe rutivi.
• Kuwedzera ose pamusoro, kunewo yoga inonyatsoita kuti kuwana nzvimbo, zvakagadzirirwa zvakananga kuti parallelogram. Rinogona kushandiswa, kana kuzivikanwa, kureba maviri dzakakwirira nhamba uye ukuru rekona pakati pavo. Zvadaro, kukwirira kuti ngazviwande pamwe nemumwe uye Sine ari pakona pakati pavo. Zvinokosha kucherechedza kuti unogona kushandisa nzira iyi yose nenhamba, izvo chokuita parallelograms (kureva, rectangle, rhombus uye dzakaenzana).

Other ehupfumi quadrangles: yakanyorwa uye circumscribed madenderedzwa

Zvatakurukura unhu uye zvivako ane quadrangle sezvo pezvakaita Euclidean geometry, zvinokosha achiteerera zvichiita kutsanangura rwakapoteredza kana kupinda mukati zvinotevera:

• Kana kuwanda wausina pamakona ose munhu chimuka zana namakumi masere madhigirii uye vakaenzana vakataurirana, zvinokwanisika kutsanangura denderedzwa vakasununguka kumativi quadrangle ichi.
• Maererano Ptolemy kuti theorem no, kana zvinorondedzerwa denderedzwa kunze polygon mativi mana, nezvibereko zvomunda diagonals vakaenzana uwandu zvibereko pakatarisana kumativi nhamba. Nokudaro, nzira yaizova: CM X LN = KL X MN + LM X KN.
• Kana ukavaka rectangle umo Verengai wausina mativi vakaenzana vakataurirana, ipapo zvinokwanisika kuinyora denderedzwa.

Wakabata pamwe yokuti rakadaro quadrilateral iro mhando zviri, ndeapi vane pamakona zvakanaka chete pakati mapato uye chii zvivako zvavanazvo, vanofanira kuyeuka zvinhu zvose izvi. Akanyanya payakavakirwa kuwana mukomberedzo uye nzvimbo polygons vaiona. Pashure pezvose, mufananidzo chimiro ichi - mumwe rakajairika, uye zivo iyi inogona kubatsira kuti Masvomhu muupenyu chaihwo.