Hurefu hwemakona matatu ekurudyi

Muchinyorwa chino, isu tichatarisa hukuru hwehurefu hwehutatu hwekurudyi, uye zvakare kuongorora mienzaniso yekugadzirisa matambudziko pane iyi nyaya.

Cherechedza: triangle inonzi rexangular, kana imwe yemakona ayo yakarurama (yakaenzana ne90 °) uye mamwe maviri ari acute (<90 °).

Hurefu zvivakwa mugonyo rekurudyi

Chivakwa 1

Triangle yekurudyi ine hurefu huviri (h₁ и h₂) inopindirana nemakumbo ayo.

hurefu hwechitatu (h₃) inodzika kune hypotenuse kubva pakona yekurudyi.

Chivakwa 2

The orthocenter (point of intersection of heights) yekona yekona yekurudyi iri pa vertex yekona yekurudyi.

Chivakwa 3

Kureba kwegonyonhatu yekurudyi yakadhonzwa kune hypotenuse inoipatsanura kuita makona matatu ekurudyi akafanana, akafananawo neaya ekutanga.

1. △US ~ △ABC pamakona maviri akaenzana: ∠ADB = ∠LAC (mitsetse yakarurama), ∠US = ∠ABC.

2. △ADC ~ △ABC pamakona maviri akaenzana: ∠ADC = ∠LAC (mitsetse yakarurama), ∠CDA = ∠ACB.

3. △US ~ △ADC pamakona maviri akaenzana: ∠US = ∠DAC, ∠BAD = ∠CDA.

Humbowo: ∠BAD = 90° – ∠ABD (ABC). Panguva imwe chete ∠ACD (ACB) = 90° – ∠ABC.

Naizvozvo, ∠BAD = ∠CDA.

Inogona kuratidzwa nenzira yakafanana iyo ∠US = ∠DAC.

Chivakwa 4

Mukona yekona yekurudyi, kureba kunokweverwa kune hypotenuse kunoverengwa sezvizvi:

1. Kuburikidza nezvikamu pane hypotenuse, yakaumbwa semhedzisiro yekukamurwa kwayo nechepasi pehurefu:

2. Kuburikidza nehurefu hwemativi egonyo:

Iyi fomula inotorwa kubva Hunhu hwe sine ye acute angle mugonyo rekurudyi (sine yekona yakaenzana nereshiyo yegumbo rakatarisana ne hypotenuse):

Cherechedza: kukona yekona yekurudyi, hurefu hwakazara hunoratidzwa mune yedu chinyorwa - zvinoshandawo.

Muenzaniso wedambudziko

Basa 1

Iyo hypotenuse yekona yekona yekurudyi yakakamurwa nehurefu hwakakweverwa kwairi kuita zvikamu 5 uye 13 cm. Wana hurefu hwehurefu uhu.

mhinduro

Ngatishandisei fomula yekutanga inoratidzwa mukati Chivakwa 4:

Basa 2

Makumbo ekona yekona ari 9 ne12 cm. Wana hurefu hwehurefu hwakakweverwa kune hypotenuse.

mhinduro

Kutanga, ngatitsvagei kureba kweiyo hypotenuse pamwe chete (regai makumbo ematatu ave “Ku” и "B", uye hypotenuse iri "vs"):

c² =A² + b² = 9² + 12² = 225.

Nekudaro, iyo с = 15cm.

Iye zvino tinogona kushandisa fomula yechipiri kubva Properties 4zvakurukurwa pamusoro apa: