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Теорема на Талес

Теорема на Талес. Теорема за ъглополовяща в триъгълник. Самостоятелна работа на IX “A” клас. Задача 1 А). Дадено : MN = 4 , BN = 9 , BN = MC Търсим : AN = ? , AB = ?, AC = ? Решение : Тр. ABC MN || BC ( M лежи на AC , N лежи на AD ) T AN/ NB = AM/MC x/9 =4/x X 2 = 36

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Теорема на Талес

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  1. Теорема на Талес Теорема за ъглополовяща в триъгълник

  2. Самостоятелна работа на IX “A” клас

  3. Задача 1 А) • Дадено : • MN = 4 , BN = 9 , BN = MC • Търсим : • AN = ? , AB = ?, AC = ? • Решение : • Тр. ABC MN || BC ( M лежи на AC , N лежи на AD ) • TAN/ NB = AM/MC • x/9 =4/x • X2 = 36 • X = 6 • AN = 6 , AB = 15 , AC = 10

  4. Б) • Дадено : • AN : NB = 2 : 3, AB = 15 • Търсим : • AM , MC , AB = ? • Решение : • 2x + 3x = 15 5x=15 x = 3 • AN = 2.3 = 6 • NB = 3.3 = 9 • AN/AM = BN/MC 6/AM=9/MC MC/AM =9/6=3/2

  5. Задача 2 : • Дадено: • Тр. ABC , BC = 8 , CA = 6 , AB = 7 , CL =l ъгъл C • Т->CA/AL=CB/LB=6x=8/7-x • 42+6x+8x=0 • 14x=42 • X=42/14=3

  6. Задача 3: • Тр.ABC,cl=l+c • AL:LB=3:4 ,AB=7см.,AC=6см.,BC=?,P=?см. • 3x+4x=7x=7 • X=1 AL=3,BL=4,AC/AL=CB/BL, 6/3=x/4 • 3x=6.4 BC=8 3x=2.4=8 P тр.6+7+8=21см.

  7. Задача 4 : Тр.ABC AC=BC,Al=C ъгъл a; BC:AB=2:1 BC:AB=2:1 AB/BL=AC/CL x/4=2x/2x-4 X(2x-4)=4.2x 2x-12x=0/:2 X-6x=0 X(x-6)=0 x=0,x=6 AB=6 AC=AB=12 P тр.=12+12+6=30см.

  8. Задача 5 : тр.ABC,P тр.=20,CL=l ъгъл c (L e AB),AL=3 ,BL=5 AB=AL+LB AB=3+5=8 AC+BC=20-8=12 AC=x BC=12-x x/3=12-x/5 5x=3(12-x) 5x=36-3x 8x=36 X=4,5 AC=4,5 BC=12-4,5=7,5

  9. Задача 6 : Тр.АBC CD=l ъгъл c(D=AB) AC=+3 P=? CA/AB=CB/BD 2/x=x+3/2 2.2=x(x+3) 4=x2+3x X2+3x-4=0 A=1 b=3 c=-4 D=9+16=25=25=5 X12=-3+-5=1,-4 OTG.1x e решение

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