Kulolu shicilelo, sizocubungula enye ye-theorems eyinhloko ekilasini lesi-7 geometry - mayelana ne-engeli yangaphandle kanxantathu. Sizophinde sihlaziye izibonelo zokuxazulula izinkinga ukuze sihlanganise indaba ethulwayo.
Incazelo yekhona langaphandle
Okokuqala, masikhumbule ukuthi liyini ikhona langaphandle. Ake sithi sinonxantathu:
Eduze nekhona langaphakathi (λ) i-engeli engunxantathu ku-vertex efanayo zangaphandle. Emfanekisweni wethu, kuboniswa ngohlamvu γ.
Lapho:
- isamba lala ma-engeli ngamadigri angu-180, okungukuthi c+ λ = 180° (impahla yekhona elingaphandle);
- 0 и 0.
Isitatimende sethiyori
I-engeli yangaphandle kanxantathu ilingana nesamba sama-engeli amabili kanxantathu angasondelene nawo.
c = a + b
Kusukela kule theory kulandela ukuthi i-engeli yangaphandle kanxantathu inkulu kunanoma yimaphi ama-engeli angaphakathi angasondelene nayo.
Izibonelo zemisebenzi
Umsebenzi 1
Unxantathu unikezwa lapho amanani ama-engeli amabili aziwa - 45 ° no-58 °. Thola i-engeli yangaphandle eduze ne-engeli engaziwa kanxantathu.
Isixazululo
Ukusebenzisa ifomula ye-theorem, sithola: 45 ° + 58 ° = 103 °.
Umsebenzi 1
I-engeli yangaphandle kanxantathu ingu-115°, kanti enye yama-engeli angaphakathi angasondelene ingu-28°. Bala amanani ama-engeli asele kanxantathu.
Isixazululo
Ukuze kube lula, sizosebenzisa i-notation eboniswe kwizibalo ezingenhla. I-engeli yangaphakathi eyaziwayo ithathwa njenge α.
Ngokusekelwe ku-theorem: β = γ – α = 115° – 28° = 87°.
I-Angle λ incikene nengaphandle, ngakho-ke ibalwa ngefomula elandelayo (ilandela kusuka endaweni yekhona elingaphandle): λ = 180° – γ = 180° – 115° = 65°.