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Sia ? 7 months, 1 week ago
विज्ञान (Science) का शाब्दिक अर्थ - वस्तु का व्यवस्थित ज्ञान है। विज्ञान शब्द की उत्पत्ति लैटिन भाषा के शब्द Skientia से हुई है , जिसका अर्थ है - ज्ञान या जानना। ... इससे यह स्पष्ट होता कि प्रकृति में पाई जाने वाली वस्तुओं एवं इनमें होने वाली अनेक घटनाओं का अध्ययन या ज्ञान प्राप्त करना ही विज्ञान है।
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Sia ? 7 months, 1 week ago
दिया है : सर्वांगसम वृत्तों की दो जीवाएँ AB तथा CD इस प्रकार है कि इन जीवाओं द्वारा वृत्तों के केंद्र O तथा O’ पर अंतरित कोण बराबर होते हैं।
सिद्ध करना है : AB = CD
उपपत्ति :
ΔAOB तथा ΔCO'D में,
∠AOB = ∠CO'D (दिया है)
OA = O'C (सर्वांगसम वृत्तों की त्रिज्या)
OB = O'D (सर्वांगसम वृत्तों की त्रिज्या)
∴ ΔAOB ≅ ΔCO'D (SSS सर्वांगसमता नियम द्वारा)
AB = CD (CPCT द्वारा)
अतः सर्वांगसम वृत्तों की जीवाएँ उनके केन्द्रों पर बराबर कोण अंतरित करें, तो जीवाएँ बराबर होती हैं।
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