Kaddarorin tsayi na triangle dama

A cikin wannan ɗaba'ar, za mu yi la'akari da mahimman kaddarorin tsayi a cikin madaidaicin alwatika, da kuma nazarin misalan warware matsalolin kan wannan batu.

lura: ana kiran triangle murabba'i, idan daya daga cikin kusurwoyinsa daidai ne (daidai da 90°) sauran biyun kuma suna da girma (<90°).

Kaddarorin tsayi a cikin madaidaicin alwatika

Kadarori 1

Triangle dama yana da tsayi biyu (h₁ и h₂) yayi daidai da kafafunsa.

tsayi na uku (h₃) saukowa zuwa hypotenuse daga kusurwar dama.

Kadarori 2

Ƙaƙwalwar ƙaƙƙarfan (matsayin tsaka-tsakin tsayi) na triangle dama yana a ƙarshen kusurwar dama.

Kadarori 3

Tsayin da ke cikin madaidaicin alwatika da aka zana zuwa hypotenuse ya raba shi zuwa madaidaitan triangles guda biyu masu kama da na asali.

1. △ABD ~ △ABC a kusurwoyi daidai gwargwado: ∠ADB = ∠LAC (layi madaidaiciya), ∠ABD = ∠ABC

2. △Dogarin ~ △ABC a kusurwoyi daidai gwargwado: ∠Dogarin = ∠LAC (layi madaidaiciya), ∠CDA = ∠Rahoton da aka ƙayyade na ACB.

3. △ABD ~ △Dogarin a kusurwoyi daidai gwargwado: ∠ABD = ∠DAC, ∠BAD = ∠CDA.

Tabbas: ∠BAD = 90 ° - ∠ABD (ABC). A lokaci guda ∠ACD (ACB) = 90 ° - ∠ABC.

Don haka, ∠BAD = ∠CDA.

Ana iya tabbatar da haka ta hanyar da ∠ABD = ∠DAC.

Kadarori 4

A cikin madaidaicin triangle, ana lissafta tsayin da aka zana zuwa hypotenuse kamar haka:

1. Ta hanyar sassa akan hypotenuse, an kafa shi ne sakamakon rabonsa da tushe na tsayi:

2. Ta tsawon bangarorin triangle:

An samo wannan tsari daga Properties na sine na m kwana a cikin madaidaicin alwatika (kwanakin kwana yayi daidai da rabon kishiyar kafa zuwa hypotenuse):

lura: zuwa madaidaicin alwatika, madaidaicin kaddarorin tsayi da aka gabatar a cikin littafinmu - kuma ana amfani da su.

Misalin matsala

Aiki 1

An raba hypotenuse na triangle dama ta tsayin da aka zana zuwa gare shi zuwa sassa 5 da 13 cm. Nemo tsawon wannan tsayin.

Magani

Bari mu yi amfani da dabara ta farko da aka gabatar a ciki Kadarori 4:

Aiki 2

Ƙafafun triangle dama 9 da 12 cm ne. Nemo tsayin tsayin da aka zana zuwa hypotenuse.

Magani

Na farko, bari mu nemo tsawon hypotenuse tare (bari kafafun triangle su kasance "zuwa" и "B", da kuma hypotenuse "vs"):

c² = A ba² + b² = 9² + 12² = 225.

A sakamakon haka, с = 15cm.

Yanzu za mu iya amfani da na biyu dabara daga Kayayyaki 4An tattauna a sama: