It is given that in triangles 𝐴𝐵𝐶 and 𝐷𝐸𝐹, $\frac{A B}{D E} = \frac{B C}{F D}$ , they will be similar if

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∠𝐴 = ∠𝐹

∠𝐵 = ∠𝐷

∠𝐵 = ∠𝐸

∠𝐴 = ∠𝐷

answer is C.

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Detailed Solution

We are given that in triangles 𝐴𝐵𝐶 and 𝐷𝐸𝐹, $\frac{A B}{D E} = \frac{B C}{F D}$
So, we can say that 𝐴𝐵 and 𝐷𝐸 are similar and 𝐵𝐶 and 𝐹𝐷 are similar.
To make the triangles 𝐴𝐵𝐶 and 𝐷𝐸𝐹 similar by 𝑆𝐴𝑆 criterion, the angle between 𝐴𝐵 and 𝐵𝐶
& 𝐷𝐸 and 𝐹𝐷 must be equal.
The angle between 𝐴𝐵 and 𝐵𝐶 is ∠𝐵, and between 𝐷𝐸 and 𝐹𝐷 is ∠𝐷.
To make the two triangles similar, these two angles must be similar, that is, ∠𝐵 = ∠𝐷.
Hence, the correct option is (c) ∠𝐵 = ∠𝐷.