Thales 'theorem: kuumbwa uye muenzaniso wekugadzirisa dambudziko

Mubhuku rino, tichatarisa imwe yedzidziso huru mukirasi 8 geometry - iyo Thales theorem, iyo yakagamuchira zita rakadaro mukukudza kwechiGiriki nyanzvi yemasvomhu uye muzivi Thales weMiletus. Tichaongororawo muenzaniso wekugadzirisa dambudziko rekubatanidza zvinyorwa zvinoratidzwa.

Chirevo che theorem

Kana zvikamu zvakaenzana zvikayerwa pane imwe yemitsetse miviri yakatwasuka uye mitsara inofambirana ichidhirowewa nemumigumo yadzo, vozoyambuka mutsetse wechipiri wakatwasuka vanocheka zvikamu zvakaenzana pairi.

• A₁A₂ =A₂A₃ ...
• B₁B₂ =B₂B₃ ...

Cherechedza: Mharadzano yezvikamu zviviri haina basa, kureva kuti theoremu ndeyechokwadi pamitsetse inopindirana uye kune inofambirana. Nzvimbo yezvikamu pane secants hainawo kukosha.

Generalized kuumbwa

Thales' theorem inyaya yakakosha proportional segment theorems*: mitsetse yakafanana inocheka zvikamu zvakaenzana pazvikamu.

Maererano neizvi, kudhirowa yedu pamusoro, kuenzana kunotevera ichokwadi:

* nekuti zvikamu zvakaenzana, kusanganisira, zvinoenzana necoefficient of proportionality yakaenzana nerimwe.

Inverse Thales theorem

1. Zvekuyambuka masendi

Kana mitsetse ikapesanisa mimwe mitsetse miviri (yakafanana kana kuti kwete) yocheka zvikamu zvakaenzana kana zvakaenzana pairi, kutanga kubva kumusoro, zvino mitsetse iyi inofanana.

Kubva pane inverse theorem inotevera:

Chimiro chinodiwa: zvikamu zvakaenzana zvinofanira kutanga kubva kumusoro.

2. Zvemasenditi anoenderana

Zvikamu pazvikamu zviviri zvinofanira kuenzana. Muchiitiko ichi chete theorem inoshanda.

• a || b
• A₁A₂ =B₁B₂ =A₂A₃ =B₂B₃ ...

Muenzaniso wedambudziko

Kupihwa chikamu AB pamusoro. Igovane muzvikamu zvitatu zvakaenzana.

mhinduro

Tora kubva pane imwe pfungwa A chaipoipo a womaka pairi zvikamu zvitatu zvakatevedzana zvakaenzana: AC, CD и DE.

yakanyanya point E pamutsetse wakatwasuka a batanidza nedot B pachikamu. Mushure meizvozvo, kuburikidza nemapoinzi asara C и D Parallel BE dhirowa mitsetse miviri inopindirana chikamu AB.

Mapoinzi ekuyambuka akaumbwa nenzira iyi pachikamu AB anochipatsanura kuita zvikamu zvitatu zvakaenzana (maererano neThales theorem).