Question

Use the given information in the figure to determine whether or not BD || AE.

Answer 1

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:

`(BC)/(AC)=(CD)/(CE)=(EA)/(DB)`

Substitute the value :

`\begin{gathered} (BC)/(AC)=(CD)/(CE)=(EA)/(DB) \\ (9)/(9+6)=(11)/(11+3)=(EA)/(DB) \\ (9)/(12)=(11)/(14)=(EA)/(DB) \\ \text{ Since the ratio are not equal} \end{gathered}`

So, the triangles are not similar thus, the lines BD is not parallel to AE

Answer : D