यदि \(\Delta ABC \cong \Delta PQR\), BC = 6 सेमी, और \(\angle A = {75^o}\) है, तो निम्न में से कौन-सा सत्य है?

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SSC CGL 2022 Tier-I Official Paper (Held On : 09 Dec 2022 Shift 3)
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  1. \(QR = 6cm,\angle R = {75^o}\)
  2. \(QR = 6cm,\angle Q = {75^o}\)
  3. \(QR = 6cm,\angle P = {75^o}\)
  4. \(PR = 6cm,\angle P = {75^o}\)

Answer (Detailed Solution Below)

Option 3 : \(QR = 6cm,\angle P = {75^o}\)
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Detailed Solution

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दिया गया है:

\(\Delta ABC \cong \Delta PQR\)

BC = 6 सेमी 

\(\angle A = {75^o}\)

प्रयुक्त अवधारणा:

दो त्रिभुजों को सर्वांगसम कहा जाता है यदि तीनों संगत भुजाएँ समान होती हैं और तीनों संगत कोण माप में समान होते हैं।

गणना:

यदि त्रिभुज ABC और PQR सर्वांगसम हैं, तो

qImage640d8176a3ca76bda91fa2aa

∠A = ∠Q और ∠B = ∠R

Δ PQR की भुजा QR, Δ ABC की भुजा BC के बराबर होनी चाहिए ताकि दोनों त्रिभुज सर्वांगसम हो जाएँ। 

\(QR = 6cm,\angle P = {75^o}\)

अतः, सही उत्तर विकल्प (3) है।

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