Answer:
no
Step-by-step explanation:
The triangles are only similar if B lies on AD and C lies on AE.
There is nothing in the given information indicating B lies on AD, or that C lies on AE. AB and BD are identified as separate segments, so don't necessarily lie on the same line. C is not identified as being anywhere in particular. "The figure shown" cannot be assumed to have any characteristics not specifically identified.
_____
Comment on the problem
The answer depends somewhat on the context of the problem. If this comes from course material in which you are routinely asked to make assumptions about figures, then the correct answer here is probably "yes." If this comes from course material that expects you to exercise critical thinking and to make no assumptions about geometrical figures, then the answer here is definitely "no."
In my opinion, one of the main purposes of studying math is to learn critical thinking—to pay attention to given facts and any assumptions you need to make.
