If in \(\triangle \mathrm{ABC} \text { and } \triangle \mathrm{DEF}\)\(\frac{A B}{D E}=\frac{B C}{F D}\) then they will be similar when:
 

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SSC CGL 2023 Tier-I Official Paper (Held On: 19 Jul 2023 Shift 3)
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  1. \(\angle B=\angle D\)
  2. \(\angle A=\angle D\)
  3. \(\angle A=\angle F\)
  4. \(\angle B=\angle E\)

Answer (Detailed Solution Below)

Option 1 : \(\angle B=\angle D\)
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Detailed Solution

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Given :

\(\frac{A B}{D E}=\frac{B C}{F D}\)

Calculation : 

If the angle made by both the sides of each triangle are equal to each other then triangle ΔABC and ΔDEF will become similar.

Hence ∠B should be equal to angle ∠D

So, ∠B = ∠D

∴ The correct answer is ∠B = ∠D.

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