Answer:
[tex]\overline {DE} \parallel \overline{AB}[/tex] because [tex]\frac{EC}{DC} = \frac{AC}{BC}[/tex].
Step-by-step explanation:
According to the Theorem of Thales and definition of proportionality, [tex]\overline {DE} \parallel \overline{AB}[/tex] if and only if [tex]\frac{EC}{DC} = \frac{AC}{BC}[/tex]. If we know that [tex]EC = 15\,cm[/tex], [tex]DC = 20\,cm[/tex], [tex]BC = 36\,cm[/tex] and [tex]AC = 27\,cm[/tex], then we have the following result:
[tex]\frac{15\,cm}{20\,cm} = \frac{27\,cm}{36\,cm}[/tex]
[tex]\frac{3}{4} = \frac{3}{4}[/tex]
Hence, [tex]\overline {DE} \parallel \overline{AB}[/tex].
