Let the lines BD || AE
So, the triangle ACE is similar to triangle BCD
Then from the properties of similar triangle
The ratio of corresponding sides are always equal:
[tex]\frac{BC}{AC}=\frac{CD}{CE}=\frac{EA}{DB}[/tex]Substitute the value :
[tex]\begin{gathered} \frac{BC}{AC}=\frac{CD}{CE}=\frac{EA}{DB} \\ \frac{9}{9+6}=\frac{11}{11+3}=\frac{EA}{DB} \\ \frac{9}{12}=\frac{11}{14}=\frac{EA}{DB} \\ \text{ Since the ratio are not equal} \end{gathered}[/tex]So, the triangles are not similar thus, the lines BD is not parallel to AE
Answer : D
