Exercițiul 8............................

Răspuns

Explicație pas cu pas:

a)Aplicam T. fundamentala de asemanare:

Daca MN║BC=> ΔAMN asemenea ΔABC

=> AM/AB=AN/AC=MN/BC

in   AM/AB=MN/BC inlocuim => 12/AB=10/20  => AB=20·12/10=24cm

=> MB=AB-AM=24-12=12cm.

in  AN/AC=MN/BC inlocuim  => AN/16=10/20 => AN=16·10/20=8cm

=>  NC=16cm-8cm=8cm.

Observam ca MN=1/2 BC => MN-linie mijlocie in ΔABC

Dupa acelasi principiu se rezolva celelalte puncte.

Răspuns

ΔAMN asemenea ΔABC ⇒AM/AB = AN/AC = MN/BC ; BM = AB-AM ;  NC = AC-AN ;

a) 12/AB = AN/16 = 10/20 = 1/2 ; AB = 12X2 = 24 CM ; AN = 16/2 = 8CM ; BM = 24-12 = 12CM ; NC = 16-8 = 8CM ;

b) AM = 24-18 = 6CM ; 6/24 = 9/AC = 8/BC ; AC = 24X9/6 = 36CM ; BC = 24X8/6 = 32 CM ; NC = 36-9 = 27CM ;

c) 10/30 = AN/36 = MN/24 ; AN = 36/3 = 12 CM ; MN = 24/3 = 8 CM ; BM = 30-10 = 20CM ; NC = 36-12 = 24CM ;

d) AB = 8+12 = 20CM ; 10/20 = AN/30 = MN/35 ; AN = 30/2 = 15CM ; MN = 35/2 = 17,5CM ; NC = 30-15 = 15 CM ;