A cikin wannan ɗaba'ar, za mu yi la'akari da ɗaya daga cikin manyan jigogi a cikin lissafi na aji 7 - game da kusurwar waje na triangle. Za mu kuma bincika misalan magance matsalolin don ƙarfafa abin da aka gabatar.
Ma'anar kusurwar waje
Da farko, bari mu tuna menene kusurwar waje. Bari mu ce muna da triangle:
Kusa da kusurwa na ciki (λ) kusurwar triangle a tsaye iri ɗaya ne external. A cikin adadi, an nuna shi ta hanyar wasiƙar γ.
A ciki:
- jimlar wadannan kusurwoyi sun kai digiri 180, watau c+ λ = 180° (dukiyar kusurwar waje);
- 0 и 0.
Bayanin ka'idar
Kusurwar triangle na waje yana daidai da jimlar kusurwoyi biyu na triangle waɗanda ba su maƙwabta da shi.
c = a + b
Daga wannan ka'idar ya bi cewa kusurwar waje na triangle ya fi kowane kusurwoyi na ciki waɗanda ba su da kusanci da shi.
Misalan ayyuka
Aiki 1
An ba da alwatika wanda aka san ƙimar kusurwoyi biyu - 45 ° da 58 °. Nemo kusurwar waje kusa da kusurwar da ba a sani ba na triangle.
Magani
Amfani da dabara na theorem, muna samun: 45° + 58° = 103°.
Aiki 1
Kusurwar waje na alwatika shine 115°, kuma ɗayan kusurwoyin ciki marasa kusa shine 28°. Yi lissafin ƙimar ragowar kusurwoyi na triangle.
Magani
Don dacewa, za mu yi amfani da bayanin da aka nuna a cikin alkalumman da ke sama. An dauki sansani na ciki kamar α.
Bisa ka'idar: β = γ – α = 115° – 28° = 87°.
Gina λ yana kusa da na waje, sabili da haka ana ƙididdige shi ta hanyar dabara mai zuwa (yana biyowa daga dukiyar kusurwar waje): λ = 180° – γ = 180° – 115° = 65°.