A cikin wannan ɗaba'ar, za mu yi la'akari da ma'anar, rarrabawa da kaddarorin ɗayan manyan siffofi na geometric - triangle. Za mu kuma bincika misalan magance matsalolin don ƙarfafa abin da aka gabatar.
Ma'anar triangle
Bamuda – Wannan siffa ce ta geometric a cikin jirgin sama, wanda ya ƙunshi bangarori uku, waɗanda aka samo su ta hanyar haɗa maki uku waɗanda ba sa kwance akan layi madaidaiciya. Ana amfani da alama ta musamman don nadi - △.
- Makina A, B da C sune madaidaitan triangle.
- Yankunan AB, BC da AC su ne gefuna na triangle, waɗanda galibi ana nuna su azaman harafin Latin ɗaya. Misali, AB= a, BC = b, DA = c.
- Ciki na triangle shi ne bangaren jirgin da ke daure da bangarorin triangle.
Bangaren triangle a tsaye suna samar da kusurwoyi uku, al'adar haruffan Girkanci suna nuni da su - α, β, γ Da sauransu. Saboda haka, triangle kuma ana kiransa polygon mai kusurwoyi uku.
Hakanan za'a iya nuna kusurwa ta amfani da alamar ta musamman "∠"
- α - ∠BAC ko ∠CAB
- β - ∠ABC ko ∠CBA
- γ - ∠ACB ko ∠BCA
Rarraba triangle
Dangane da girman kusurwoyi ko adadin daidaitattun bangarorin, ana rarrabe nau'ikan adadi masu zuwa:
1. m-angular – alwatika mai duk kusurwoyi uku m, watau kasa da 90°.
2. ƙi Alwatika wanda ɗaya daga cikin kusurwoyin ya fi 90° girma. Sauran kusurwoyi biyu masu tsauri ne.
3. rectangular – triangle wanda daya daga cikin kusurwoyi daidai yake, watau yayi daidai da 90°. A cikin irin wannan siffa, bangarorin biyu da suka samar da kusurwar dama ana kiran su kafafu (AB da AC). Bangare na uku da ke gaban kusurwar dama shine hypotenuse (BC).
4. m Alwatika wanda duk bangarorin ke da tsayi daban-daban.
5. Isosceles - triangle mai tarnaƙi guda biyu daidai, waɗanda ake kira a gefe (AB da BC). Bangare na uku shine tushe (AC). A cikin wannan adadi, kusurwar tushe daidai suke (∠BAC = ∠BCA).
6. Daidaitawa (ko daidai) Alwatika mai tsayi wanda dukkan bangarorin ke da tsayi iri ɗaya. Haka kuma dukkan kusurwoyinsa 60° ne.
Abubuwan Triangle
1. Duk wani gefen triangle bai kai sauran biyun ba, amma ya fi bambance-bambancen su girma. Don dacewa, mun yarda da daidaitattun zane-zane na bangarorin - a, b и с… Sannan:
b - c <a <b +cAt b > c
Ana amfani da wannan kadarar don gwada sassan layi don ganin ko za su iya samar da triangle.
2. Jimlar kusurwoyin kowane triangle shine 180°. Ya biyo bayan wannan kadarar cewa a cikin triangle obtuse kusurwoyi biyu koyaushe suna da ƙarfi.
3. A cikin kowane triangle, akwai babban kusurwa mai girma a gaban babban gefen, kuma akasin haka.
Misalan ayyuka
Aiki 1
Akwai sanannun kusurwoyi biyu a cikin alwatika, 32° da 56°. Nemo darajar kusurwa ta uku.
Magani
Bari mu dauki kusurwoyi da aka sani a matsayin α (32°) kuma β (56°), da wanda ba a sani ba – a baya γ.
Dangane da dukiya game da jimillar dukkan kusurwoyi, a + b+c = 180 °.
A sakamakon haka, γ = 180° - ba - b = 180 ° - 32 ° - 56 ° = 92 °.
Aiki 2
An ba da sassa uku na tsawon 4, 8 da 11. Gano ko za su iya samar da triangle.
Magani
Bari mu tsara rashin daidaituwa ga kowane ɓangaren da aka bayar, dangane da kadarorin da aka tattauna a sama:
11 - 4 <8 <11 + 4
8 - 4 <11 <8 + 4
11 - 8 <4 <11 + 8
Dukansu daidai ne, saboda haka, waɗannan sassan na iya zama gefen triangle.