Question

la triunghiul ABC, punctul M se află pe latura AC, MN || AB, N & BC. Completați
Labelul:
atunci
AC
BC
NC
MA
5
6
MC
4
NB
3,5
(1)
14
12
بیه
10
DAC
nem
AC
b)
e
d)
e
12
15
18
20
3
6
24

Answer 1

Răspuns:

Explicație pas cu pas:

Aplic Thales

a)MA/MC=NB/NC    ⇒5/4=3,5/x   ⇒x=4·3,5/5=2,8 cm

AC=MA+MC=5+4=9 cm

BC=NB+NC=3,5+2,8=6,3 cm

b) MC/AC=NC/BC      ⇒8/14=12/BC     ⇒BC=12·14/8=3·7=21 cm

NC=BC-NC=21-12=9 cm

MC=AC-AM=14-6=8 cm

c) NC/BC=MC/AC    ⇒5/15=3/AC    ⇒AC=15·3/5=9 cm

AM=AC-MC=9-3=6 cm

NC=BC-NB=15-10=5 cm

d)NC/BC=MC/AC   ⇒3/18=MC/12    ⇒1/6=MC/12      ⇒MC=12/6=2 cm

AM=AC-MC=12-2=10 cm

NB=BC-NB=18-3=15 cm

e) AC=AM+MC=6+24=30 cm

MC/AC=NC/BC    ⇒24/30=NC/20=4/5     ⇒NC=16 cm

NB=BC-NC=20-16=4 cm