10. If in triangles \(ABC\) and \(DEF\), \(\dfrac{AB}{DE}=\dfrac{BC}{FD}\), then they will be similar when
\(\angle B=\angle E\)
\(\angle A=\angle D\)
\(\angle B=\angle D\)
\(\angle A=\angle F\)
Step 1: To prove two triangles are similar, one common method is the SAS (Side-Angle-Side) similarity rule. It says: If two sides of one triangle are in the same ratio as two sides of another triangle, and the angle between those sides is equal, then the triangles are similar.
Step 2: Here we are given that \(\dfrac{AB}{DE} = \dfrac{BC}{FD}\). So, side \(AB\) of triangle \(ABC\) is proportional to side \(DE\) of triangle \(DEF\), and side \(BC\) is proportional to side \(FD\).
Step 3: Notice the position of these sides. In triangle \(ABC\), the angle between sides \(AB\) and \(BC\) is \(\angle B\). In triangle \(DEF\), the angle between sides \(DE\) and \(FD\) is \(\angle D\).
Step 4: For SAS similarity, we need these included angles to be equal. That means \(\angle B = \angle D\).
Final Answer: Therefore, the triangles will be similar when \(\angle B = \angle D\).