Question

consideram triunghiul ABC si punctele D apartine (AB), E apartine (AC),astfel incat DE || BC si AD supra AB= 3 supra 5. calculati valoarea rapoartelo: AD supra DB, AE supra EC, AC supra EC, AE supra AC

Answer 1

AD/AB=3/5
AB=AD+DB⇒
AD/(AD+DB)=3/5
5AD=3AD+3DB
2AD=3DB
AD/DB=3/2

AD/DB=3/2⇒AE/EC=3/2⇒

AC/EC=?
AE/AC=3/5
AE=AC-EC⇒
(AC-EC)/AC=3/5
5AC-5EC=3AC
2AC=5EC
AC/CE=5/2

AE/AC=3/5 aceasi proportie ca si AD/AC PT CA ED║BC