Uchburchaklar o‘xshashligining ikkinchi alomati — 9-sinf Geometriya test savollari

1.Uchburchak ABC va DEF da AB = 8 sm, AC = 12 sm, DE = 6 sm, DF = 9 sm, burchak A = burchak D. Bu uchburchaklar o‘xshashmi va koeffitsienti nechaga teng (ABC dan DEF ga)?

• A)O‘xshash, $k=\frac{4}{3}$
• B)O‘xshash emas
• C)O‘xshash, $k=\frac{3}{4}$
• D)O‘xshash, $k=\frac{2}{3}$

2.Uchburchak ABC ~ uchburchak A₁B₁C₁ (ikkinchi alomat bo‘yicha), AB/A₁B₁ = AC/A₁C₁ $=\frac{5}{2}$, burchak A = burchak A₁. Agar A₁B₁ = 4 sm bo‘lsa, AB ni toping.

• A)1,6 sm
• B)20 sm
• C)8 sm
• D)10 sm

3.Uchburchak ABC da AB = 10 sm, AC = 15 sm, burchak A = 40°. Uchburchak MNP da MN = 6 sm, MP = 9 sm, burchak M = 40°. Bu ikki uchburchak o‘xshashligini isbotlash uchun qaysi alomat ishlatiladi?

• A)Pifagor teoremasi
• B)Ikkinchi alomat (ikki tomon proporsional va ular orasidagi burchak teng)
• C)Birinchi alomat (ikki burchak teng)
• D)Uchinchi alomat (uch tomon proporsional)

4.Uchburchak ABC va DEF da AB/DE = BC/EF $=\frac{3}{5}$, burchak B = burchak E. Agar BC = 9 sm bo‘lsa, EF ni toping.

• A)5,4 sm
• B)27 sm
• C)3 sm
• D)15 sm

5.Uchburchak ABC ~ uchburchak A₁B₁C₁, AB = 6 sm, A₁B₁ = 18 sm, AC = 4 sm. A₁C₁ ni toping (ikkinchi alomat: AB/A₁B₁ = AC/A₁C₁, burchak A = burchak A₁).

• A)6 sm
• B)24 sm
• C)12 sm
• D)1,33 sm

6.Ikkinchi o‘xshashlik alomatiga ko‘ra uchburchaklar o‘xshash bo‘lishi uchun nima talab qilinadi?

• A)Ikkita tomon proporsional va ular orasidagi burchaklar teng bo‘lishi
• B)Barcha tomonlar teng bo‘lishi
• C)Ikkita burchak teng bo‘lishi
• D)Uchta tomon proporsional bo‘lishi

7.Uchburchak ABC da AB = 14 sm, AC = 21 sm. Uchburchak ADE da AD = 4 sm, AE = 6 sm, D — AB da, E — AC da, burchak A umumiy. Bu uchburchaklar o‘xshashmi?

• A)Aniqlab bo‘lmaydi
• B)Yo‘q, nisbatlar teng emas
• C)Ha, lekin faqat taxminan
• D)Ha, AD/AB = AE/AC $=\frac{2}{7}$

8.Uchburchak ABC va MNP o‘xshash (ikkinchi alomat), AB = 9 sm, MN = 12 sm, AC = 6 sm. MP ni toping.

• A)18 sm
• B)8 sm
• C)4,5 sm
• D)6 sm

9.Uchburchak ABC ~ uchburchak DEF, o‘xshashlik koeffitsienti k = 2,5 (ABC dan DEF ga). AB = 8 sm bo‘lsa, DE ni toping.

• A)3,2 sm
• B)16 sm
• C)10,5 sm
• D)20 sm

10.Uchburchak ABC va PQR da burchak A = burchak P = 65°, AB/PQ = 3, lekin AC/PR = 2. Bu uchburchaklar o‘xshashmi?

• A)Yo‘q, chunki nisbatlar teng emas
• B)Aniqlab bo‘lmaydi
• C)Ha, chunki burchak teng
• D)Ha, o‘rtacha nisbat bo‘yicha