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ત્રિકોણની સમરૂપતા
ત્રિકોણોની સમરૂપતાની વ્યાખ્યા અનુસાર bold increment bold space bold DEF અને bold increment bold space bold XYZ માટે સંગતતા bold DEF bold space bold left right arrow bold space bold ZXY સમરૂપતા થાય તે માટેની શરતો કઈ છે ?
Answer
    • bold increment bold space bold PQR અને bold increment bold space bold XYZ માટે સંગતતા bold PQR bold space bold left right arrow bold space bold YZX સમરૂપતા છે. bold m bold space bold angle bold P bold space bold equals bold space bold 2 bold m bold space bold angle bold Q અને bold m bold space bold angle bold X bold space bold equals bold space bold 120 bold. bold space bold m bold space bold angle bold Y શોધો.
    Answer
    • bold increment bold space bold ABC અને bold increment bold space bold PQR ની સંગતતા bold ABC bold space bold left right arrow bold space bold PQR સમરૂપતા છે. AB : PQ = 4:5.  જો AC = 6, તો PR શોધો. જો QR = 15,  તો BC શોધો.
    Answer
    • સંગતતા bold PQR bold space bold left right arrow bold space bold EDF માટે bold increment bold space bold PQR bold space bold tilde bold space bold increment bold space bold DEF bold. bold space જો PQ + QR = 10 અને PR = 6  હોય, તો EF શોધો.
    Answer
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    bold increment bold space bold ABC અને bold increment bold space bold PQR માં સંગતતા bold ABC bold space bold left right arrow bold space bold QPR સમરૂપતા છે. bold increment bold space bold ABCની પરિમિતિ 15 અને bold increment bold space bold PQR ની પરિમિતિ 27 છે. જો BC = 8 અને QR = 9 હોય, તો PR અને AC શોધો.
    bold increment bold space bold ABC અને bold increment bold space bold PQR ની સંગતતા bold ABC bold space bold left right arrow bold space bold QPR સમરૂપતા છે.
    bold therefore bold space bold AB over bold QP bold space bold equals bold space bold BC over bold PR bold space bold equals bold space bold AC over bold QR bold therefore bold space bold AB over bold QP bold space bold equals bold space bold BC over bold PR bold space bold equals bold space bold AC over bold QR bold space bold equals bold space fraction numerator bold AB bold space bold plus bold space bold BC bold space bold plus bold space bold AC over denominator bold QP bold space bold plus bold space bold PR bold space bold plus bold space bold QR end fraction

    bold therefore bold space bold AB over bold QP bold space bold equals bold space bold BC over bold PR bold space bold equals bold space bold AC over bold QR bold space bold equals bold space fraction numerator bold increment bold space bold ABC bold space bold ન ી bold space bold પર િ મ િ ત િ over denominator bold increment bold space bold PQR bold space bold ન ી bold space bold પર િ મ િ ત િ end fraction bold space bold space bold space bold space bold space bold BC over bold PR bold space bold equals bold space fraction numerator bold increment bold space bold ABC bold space bold ન ી bold space bold પર િ મ િ ત િ over denominator bold increment bold space bold PQR bold space bold ન ી bold space bold પર િ મ િ ત િ end fraction bold therefore bold space bold 8 over bold PR bold space bold equals bold space bold 15 over bold 27 bold therefore bold space bold space bold 8 bold space bold cross times bold space bold 27 over bold 15 bold space bold equals bold space bold PR bold therefore bold space bold PR bold space bold equals bold space bold 72 over bold 5 bold space bold therefore bold space bold PR bold space bold equals bold space bold 14 bold. bold 4 bold space bold AC over bold QR bold space bold equals bold space fraction numerator bold increment bold space bold ABC bold space bold ન ી bold space bold પર િ મ િ ત િ over denominator bold increment bold space bold PQR bold space bold ન ી bold space bold પર િ મ િ ત િ end fraction bold therefore bold space bold AC over bold 9 bold space bold equals bold space bold 15 over bold 27 bold therefore bold space bold AC bold space bold equals bold space bold 15 over bold 27 bold space bold cross times bold space bold 9 bold space bold therefore bold space bold AC bold space bold equals bold space bold 5 bold space
    Answer
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