The chiratidzo chokutanga wakaenzana zvokuridza. Zviratidzo wakaenzana zvokuridza rechipiri uye rechitatu

Pakati kuwanda polygons, izvo vanotova vasiri intersecting akavhara polygonal mutsetse, netriangle - ari mufananidzo pamwe mudukusa nhamba pamakona. Mune mamwe manzwi, ndiye nyore polygon. Asi, pasinei kwayo nyore, mufananidzo uyu anovanza hwakawanda zvakavanzika uye dzinonakidza matongo, iyo inotaura rinokosha bazi wemasvomhu - geometry. chirango ichi muzvikoro kutanga kudzidzisa giredhi rechinomwe, uye "Triangle" Musoro azopiwa kutarisirwa. Vana kwete chete kudzidza mitemo nechipi pacharo, asiwo enzanisa kudzidza 1, 2 uye 3, chiratidzo wakaenzana zvokuridza dzavo.

ruzivo rokutanga

Mumwe mitemo rokutanga, vanoziva vadzidzi, kwarinoenda chinhu chakadai: Verenga pamakona ose netriangle vakaenzana 180 inegumi. Kuti asimbise ichi, zvakatikwanira kushandisa protractor kuyera nechimwe vertices uye kuwedzera yose zvichiguma tsika. Nokudaro, apo vaviri anozivikanwa tsika nyore kuona wechitatu. Somuenzaniso: Pane imwe pakona Triangle 70 °, uye mumwe ari - 85 °, chii ukuru rechitatu yorusvingo?

180 - 85 - 70 = 25.

Pindura: 25 °.

Mabasa anogona kuva yakaoma, kana chaiyo angled ukoshi rimwe chete uye kukosha wechipiri pamusoro akati chete sei zvikuru kana kuti kazhinji zviri kupfuura zvichidzika.

Mune Triangle yokusarudza mumwe kana mumwe zvayo chaiyo zviri mutsetse mumwe nomumwe rinogona kuitwa ine zita vayo:

• kukwirira - the perpendicular mutsetse wakavhomorwa kubva vertex kusvikira kune rumwe rutivi;
• zvose zvakakwirira matatu, inoitwa panguva imwe chete iyoyo, pakati nhamba piringisha, achiumba orthocenter, iyo, zvichienderana nemhando yacho Triangle kunogona mukati nokunze;
• EvaMedhia - mutsetse unobva kumusoro pakati rumwe rutivi;
• ndiyo pfungwa mharadzano pakati medians waro zvakaoma kwazvo, ari mukati chimiro;
• bisector - mutsetse vachimhanya kubva kumusoro kusvika mharadzano nevakomana divi, pfungwa mharadzano pakati bisectors matatu ndiyo musimboti rakanyorwa denderedzwa.

Simple chokwadi pamusoro zvokuridza

Triangles, sezvo, zvirokwazvo, uye zvose nenhamba vane unhu avo uye zvivako. Sezvambotaurwa, mufananidzo uyu nyore polygon, asi pamwe yayo mamirire zvinhu:

• zvaipesana refu-divi angled nguva dzose akavata nokukura yakakura, uye vakutarisire;
• pamusoro wakaenzana kumativi vakaenzana pamakona, muenzaniso - imwe Triangle isosceles;
• Verengai mukati pamakona anogara akaenzana 180 °, kuti kare zvakaratidza pamusoro muenzaniso;
• kuripa pane rimwe divi, triangle achiumbwa mhiri rokunze angled iyo achagara akaenzana Verengai pamakona, izvozvo haana pedyo;
• mumwe mapato anogara asingasviki Verengai mamwe mativi maviri, asi dzakawanda kusawirirana kwavo.

marudzi zvokuridza

Kutsvaga inotevera Danho iri kuziva boka kuti iyo akapa Triangle. Kuva imwe mhando kunoenderana zvinokosheswa pamakona ose netriangle.

• Isosceles - kumapati vakaenzana vaviri akadana divi, wechitatu iyi anoita se chawo zvitarisiko. The pamakona ari mujinga Triangle ndiwo chete uye muMedhia akapiwa wakavhomorwa kubva pamusoro, ndiye bisector uye kukwirira.
• Rairira, kana ane equilateral, triangle - mumwe umo mativi ayo ose vakaenzana.
• Rectangular mumwe kumakona ayo 90 °. Panyaya iyi, kurutivi rwakatarisana angled ichi inonzi hypotenuse, uye vamwe vaviri - makumbo.
• Chenjera, triangle - ose pamakona asingasviki 90 °.
• Obtuse - mumwe pamakona kupfuura 90 °.

Kuenzana uye zvakafanana. zvokuridza

Mukuita kudzidza hakusi chete yoga zvaiona akatorwa chimiro, asiwo kuenzanisa zvokuridza maviri. Uye dingindira sokuti nyore ichi ane yakawanda mitemo uye theorems izvo zvinogona kwakaratidza kuti vaiona nhamba - zvakaenzana zvokuridza. Zviratidzo zvokuridza vane tsanangudzo vakaenzana: pakati zvokuridza vakaenzana kana dzavo tsamba kumativi uye pamakona vakaenzana. With mukana wokuti vanhu vanga ichi, isu kana kuisa nhamba mbiri idzi pane mumwe, mitsetse dzavo zvose wekuita. Uyewo mufananidzo angava zvakafanana, zvikurukuru, nezvezvitadzo substantially kufanana zvitarisiko, zvakasiyana chete zvikuru. Kuti kuita mhedziso zvakadaro pamusoro dzaimirirwa zvokuridza inofanira akasangana muna rimwe zvinotevera ezvinhu:

• pamakona maviri mufananidzo akaenzana pamakona maviri mumwe;
• Proportional maviri mativi maviri kumativi Triangle wechipiri, uye pamakona ose aumba mativi vakaenzana;
• mativi matatu wechipiri mufananidzo kwakafanana kuti rokutanga.

Chokwadi, nokuti undisputed kuenzana, izvo haakonzeri kuchangotanga mubvunzo, unofanira kuva tsika ine zvinhu zvose zvose nhamba, asi dambudziko dzidziso iri nyore zvikuru, uye chete mamiriro ezvinhu shoma akabvumira kuti kuratidza kuti zvokuridza.

Chiratidzo wakaenzana zvokuridza okutanga

panyaya nematambudziko zviri kugadziriswa pachishandiswa uchapupu theorem no, iyo inoti sezvinotevera: ". Kana mativi maviri Triangle, kundosvikazve pakona izvo vanoumba, vakaenzana maviri kumativi uye pakona rimwe Triangle, ipapo nhamba dziri uyewo vakaenzana imwe"

Sezvo kurira uchapupu theorem no pamusoro chiratidzo wakaenzana zvokuridza rokutanga? Munhu wose anoziva kuti zvikamu zvacho zviviri vakaenzana kana vane kuenzana, kana sekamufarenzi yakaenzana kana vane zvakafanana nharaunda. Zvino zvakaitika, triangle pane zviratidzo shoma izvo zvinogona vakafunga kuti nhamba akafanana, iyo inobatsira chaizvo kugadzirisa matambudziko geometric siyana.

Ruzha theorem no "Chiratidzo wakaenzana zvokuridza yokutanga", zvataurwa pamusoro apa, asi ayo uchapupu:

• Ngatitii, triangle ABC uye A ₁ B ₁ C ₁ vari mativi chete AB uye A ₁ B ₁ uye ukuwo, BC uye B ₁ C _1, uye dzinoita kuti vanhu inoumbwa kumativi izvi zvakafanana ukoshi, i.e. vakaenzana. Zvadaro akariisa pamusoro ABC △ △ A ₁ B ₁ C _1, tinowana machisa mitsara zvose uye vertices. It anotevera kuti zvokuridza aya zvakangofanana, zvinoreva zvakaenzana.

Theorem "Chiratidzo wakaenzana zvokuridza rokutanga," inonziwo "On mbiri panhivi uye pakona." Chaizvoizvo, izvi ndiwo payo.

Theorem pamusoro chiratidzo chechipiri

The chiratidzo wakanyatsojeka chechipiri hunoratidzwa zvakafanana, uchapupu hunobva pakuti nokuiswa zvidimbu pane mumwe, havana kufanana vose pemisoro uye mumativi. A theorem no rinonzwika seizvi: "Kana mumwe rutivi uye vaviri pamakona pakugadzirwa icho chikamu ari Party maviri kumakona Triangle wechipiri, ipapo nhamba idzi fanana, kureva vakaenzana."

The chiratidzo wechitatu uye uchapupu

Kana vose 2 uye 1 chiratidzo wakanyatsojeka unoshandawo mativi ose zvokuridza, pamakona uye zvitarisiko, rechitatu hunongotaura mapati. Saka theorem no une zvinotevera mashoko: "Kana vose kumativi netriangle vakaenzana kumativi matatu Triangle wechipiri, nenhamba akafanana."

Kuti aratidze theorem no ichi, zvinokosha yakawanda yokunyatsoongorora hukuru zvakadzama tsanangudzo wakanyatsojeka. Kutaura zvazviri, chii chinorehwa "zvokuridza vakaenzana"? Kuzivikanwa inoti kuti isu kana kumanikidza mumwe mufananidzo kune imwe, ose okunze kuenderana, zvinogona chete kuitika apo mativi avo uye pamakona vakaenzana. Panguva iyoyowo rekona pakatarisana rimwe divi, inova zvakafanana nemamwe Triangle akaenzana runoenzanirana vertex rechipiri nhamba. Zvinofanira kucherechedzwa kuti panguva iyi chinoratidza nyore kushandurira kupinda 1 chiratidzo wakaenzana zvokuridza. Kana kutevedzana uku haasi kuchengetwa, wakaenzana zvokuridza hazvitomboiti, kunze zviitiko apo nhamba girazi mufananidzo wokutanga.

Right zvokuridza

Sechivako zvokuridza zvakadaro nguva dzose vertex pamwe rekona 90 °. Saka, mashoko anotevera ndeechokwadi:

• zvokuridza kuruoko angled vakaenzana kana makumbo rechipiri cathetus fanana;
• Nhamba vakaenzana kana vachaenzana kune hypotenuse uye mumwe makumbo;
• zvokuridza dzakadaro vakaenzana kana makumbo avo uye akafanana rikwanise angled.

Nyaya iyi chokuita rectangular zvokuridza. Kuti varatidze Theorem akashandisa App zvitarisiko kune mumwe, zvichiguma makumbo zvokuridza vari akapeta kuitira kuti mbiri yakarurama kuruboshwe yakarurama angled ne CA ₁ uye CA mativi.

kushanda

Kazhinji, mune tsika, aishandiswa chiratidzo wakaenzana zvokuridza okutanga. Kutaura zvazviri, izvi kirasi sokuti nyore kuti geometry uye ndege geometry akashandisa dingindira uye 7 kuverenga urefu, somuenzaniso, foni wire pasina kuyerwa nharaunda, pazviri ngakuitwe. Tichishandisa theorem no ichi zviri nyore kuita zvakakodzera Masvomhu kuona kureba chitsuwa, riri pakati pomupata, pasina kushambira mhiri nayo. Kana kusimbisa fenzi nokuisa pakapuranga iri apo panopinda zvokuti rakakamurwa mbiri dzakaenzana zvokuridza, kana ngaaverenge zvakaoma zvinhu basa kuveza kana dzemaitirwe pakati truss padenga ezvinhu panguva kuvakwa.

Chiratidzo wakaenzana zvokuridza wokutanga une upamhi kushanda mu chaicho "mukuru" upenyu. Paaiva mumakore chesekondari ndiyo nyaya dzakawanda sokuti hakunakidzi uye zvachose zvisingakoshi.