यदि \(\triangle \mathrm{ABC} \text { and } \triangle \mathrm{DEF}\) में, \(\frac{A B}{D E}=\frac{B C}{F D}\) है, तो वे कब समरूप होंगे?
 

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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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दिया गया है:

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

गणना: 

यदि प्रत्येक त्रिभुज की दोनों भुजाओं द्वारा बनाए गए कोण एक दूसरे के बराबर हों तो त्रिभुज ΔABC और ΔDEF समरूप होंगे।

अतः, ∠B कोण ∠D के बराबर होना चाहिए।

इसलिए, ∠B = ∠D

∴ सही उत्तर ∠B = ∠D है।

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