Question

Daca se considera triunghiul ABC si punctele D si si E, D apartine (AB),E apartine (BC),astfel incat DE || AC.a) Daca DB = 4cm,AB = 10cm si BC = 15cm, calculati BE ,AD si EC.
b)Daca EC = 3 cm,BE =12 cm si AD = 6 cm,calculati DB,AB,BC.
c)BE = 7cm,AD=10cm si AB=24cm,calculati DB,EC,BC
d)Daca BD= 8cm,AD=6cm,BE=4cm,calculati AB,EC,BC.

Answer 1

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Answer 2

A. ED ll AC =>(TEOREMA LUI THALES)$\frac{BD}{AB}= \frac{EB}{BC}<= >\frac{4}{10}= \frac{EB}{15}=> EB = 6$
AD=AB-BD=6 cm
EC=BC-EB=5 cm
B.
DE ll AC=> (TEORMEA LUI THALES) =>$\frac{BD}{AD} =\frac{BE}{EC} => \frac{BD}{6} = \frac{12}{3} => BD=24$
AB=BD+AD=30
BC=BE+EC=15

C.BD=AB-AD=14
DE llAC => (TEOREMA LUI THALES) $\frac{AB}{BD} = \frac{BC}{EB} <=> \frac{24}{14} = \frac{BC}{7} =>BC= \frac{24*7}{14}=12$
EC=BC-EB=12-7=5

D.AB=BD+AD=14
DE llAC => (TEOREMA LUI THALES) =>[tex] \frac{AB}{BD} = \frac{BC}{BE} <=> \frac{14}{8} = \frac{BC}{4}=>BC= \frac{14*4}{8} =7 [/tex]
EC=BC-DE=7-4=3