Katatu kakang'ono: lingaliro ndi katundu

Yankho la mavuto a zilembo limafuna kudziwa zambiri. Chimodzi mwa matanthawuzo ofunika a sayansiyi ndi katatu yolumikizidwa bwino.

Mwa lingaliro limeneli ndikutanthauza chiwerengero cha chijerengero chokhala ndi maanga atatu Zopanda, ndipo mtengo wa pangodya imodzi ndi madigiri 90. Maphwando omwe ali ndi ngodya yolondola amachititsa mayina a mwendo, chipani chachitatu, chotsutsana nacho, chimatchedwa hypotenuse.

Ngati miyendo mu chiwerengero ichi ndi ofanana, imatchedwa isosceles katatu yolondola. Pachifukwa ichi, pali zofunikira ku mitundu iwiri ya katatu, zomwe zikutanthauza kuti katundu wa magulu awiriwo amalemekezedwa. Kumbukirani kuti mazenera omwe ali pansi pa isosceles katatu amakhala olingana nthawi zonse, choncho amphuno akuthwawo angaphatikizepo madigiri 45.

Kukhalapo kwa chimodzi mwa zinthu zotsatirazi kumatithandiza kuti tiwonetse kuti katatu kamodzi katatu kamodzi kamodzi ndi kamodzi:

1. Miyendo ya katatu awiri ndi ofanana;
2. Zizindikiro zili ndi zofanana zofanana ndi imodzi ya miyendo;
3. Zogwirizana ndi zomwe zimakhala zovuta komanso zinazake zazing'ono;
4. Mkhalidwe wofanana wa mwendo ndi ngodya yaikulu amawonedwa.

Dera la katatu loyendetsedwa bwino likhoza kuwerengedwa mosavuta ndi chithandizo cha machitidwe ofanana, komanso ngati mtengo wofanana ndi theka la miyendo yake.

Pa katatu yolumikizidwa bwino, maubwenzi otsatirawa ndi awa:

1. Cathet ndichabechabechabe pokhapokha pokhapokha ndikuyang'anapo;
2. Ngati tikulongosola bwalo pozungulira katatu yolondola, likulu lake lidzakhala pakati pa chiwonetsero;
3. Kutalika komwe kumachokera kumbali yolondola ndiko kulingalira kwapakati kwapadera kwa miyendo ya katatu ku lingaliro lake.

N'zochititsa chidwi kuti, ngakhale pang'onopang'ono yolumikizidwa bwino, izi zimapezeka nthaŵi zonse.

The Pythgorore Theorem

Kuwonjezera pa zida zapamwamba za katatu, zizindikiro izi ndizo: chiwerengero cha hypotenuse ndi chofanana ndi miyendo ya miyendo. Theorem imeneyi imatchedwa dzina lake woyambitsa - theorem ya Pythagoras. Anapeza mgwirizano umenewu pamene anali kuphunzira malo a malo omwe anamangidwa pambali pa katatu yolondola.

Pofuna kutsimikizira theorem, timapanga katatu ABC, miyendo yake yomwe imatchulidwa ndi a ndi b, ndi hypotenuse c. Kenako, timangapo malo awiri. Mbali imodzi idzakhala ndi hypotenuse, ina imakhala miyendo iwiri.

Kenaka dera loyamba lapafupi lingapezeke m'njira ziwiri: monga chiwerengero cha mbali zitatu za katatu ABC ndi malo achiwiri, kapena ngati mbali, ndi zachibadwa kuti izi zifanana. Ndiko:

Ndi ² + 4 (ab / 2) = (a + b) ² , timasintha ndondomekoyi:

Ndi ² + 2 ab = a ² + b ² + 2 ab

Zotsatira zake, timapeza: ndi ² = ² + b ²

Choncho, chiwerengero chajimidwe cha katatu chokongoletsera sichimagwirizana ndi katundu yense wokhala ndi katatu. Kukhalapo kwa ngodya yolondola kumapangitsa kuti chiwerengerocho chikhale ndi ubale wina wapadera. Kuphunzira kwawo kuli kothandiza osati sayansi yokha, komanso mu moyo wa tsiku ndi tsiku, chifukwa chokhala ngati katatu kakang'ono, kamapezeka paliponse.