Explicație pas cu pas:
14.
AB/[tex]A_{1}B_{1}[/tex]=4/3 =>[tex]A_{1}B_{1}[/tex]=3AB/4=3*16/4=12 cm
BC/[tex]B_{1}C_{1}[/tex]=4/3 =>[tex]B_{1}C_{1}[/tex]=3BC/4=3*20/4=15 cm
∡B=∡[tex]B_{1}[/tex]
AB/[tex]A_{1}B_{1}[/tex]=BC/[tex]B_{1}C_{1}[/tex] →ΔABC asemenea cu Δ[tex]A_{1}B_{1} C_{1}[/tex]
Atunci AC/[tex]A_{1}C_{1}[/tex]=BC/[tex]B_{1}C_{1}[/tex] →[tex]A_{1}C_{1}[/tex]=3AC/4=3*24/4=18 cm
15.
AM= 2 cm
MB= 8 cm
AN= 3 cm
NC= 12 cm
AB=AM+MB=10 cm
AC=AN+NC=15 cm
AM/AB=2/10=1/5 |
AN/AC=3/15=1/5 }=>triunghiuri asemenea
Triunghiurile ΔAMN si ΔABC au un unghi comun, ∡A |
si raportul de asemanare este 1/5
