Question

Ex 1. f);g);h) ex 8,9,10,11,12,13

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Answer 1

Răspuns:1.

f)ΔMKF:m=66°,k=f

66°+2k=180°

k=114/2

k,f=57°

k=f⇒triunghiul este isoscel

g)ΔAOB: a=o=b

a=o=b⇒ΔAOB echilateral⇒a=o=b=60°

h)ΔEFG: e=27°,f=63°

g+27°+63°=180°

g=180-90

g=90°⇒triunghiul este dreptunghic

8.

c=90°

a=2*b

a+b+c=180°

2*b+b+90°=180°

3b=90°

b=30°

a=2*30=60°

9.

a=120°

b=3*c

a+b+c=180°

120°+3c+c=180

4c=60°

c=15°

b=3*15=45°

10.

c=40°

a/b=2/3

2b=3a

b=3a/2

a+b+c=180°

a+3a/2+40°=180°  (aducem la acelasi numitor)

2a/2+3a/2=280°/2

5a/2=280°/2

5a=280°

a=56°

b=3*56/2

b=84°

11.

a+b+c=180  

a/5=b/6=c/7=(a+b+c)/(5+6+7)=180/18=10

a=5x10=50

b=6x10=60

c=7x10=70

12.

m/2+2/4+p/6 = k

m = 2k ; n = 4k ; p = 6k ;

m+n+p = 180°

2k+4k+6k = 180°

12k = 180°

k = 180°/12 = 15°

m = 2x15° = 30°

n = 4x15° = 60°

p = 6x15° = 90° ⇒ triunghiul este dreptunghic

13.

{a,b,c}i.p.{1/4,15/90,125/1000}

a*(1/4)=k

a/4=k

a=4k

b*(15/90)=k

15b/90=k

b=90k/15(inversul fractiei)

b=6k

c*(125/1000)=k

125c/1000=k

c=1000k/125(innversul fractiei)

c=8k

a+b+c=180

4k+6k+8k=180

18k=180

k=180:18

k=10

a=10*4

a=40°

b=10*6

b=60°

c=10*8

c=80°