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Class 10 Class 12

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 ?

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.

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.

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.

$bold increment bold space bold PQR$ અને $bold increment bold space bold DEF$ ની સંગતતા $bold PQR bold space bold left right arrow bold space bold EDF$ સમરૂપતા છે.

$bold therefore bold space bold PQ over bold ED bold space bold equals bold space bold QR over bold DF bold space bold equals bold space bold PR over bold EF bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold. bold. bold. bold space bold left parenthesis bold 1 bold right parenthesis bold space bold હવ ે bold comma bold space bold PQ over bold ED bold space bold equals bold space bold QR over bold DF bold space bold therefore bold space bold PQ over bold ED bold space bold equals bold space bold QR over bold DF bold space bold equals bold space fraction numerator bold PQ bold space bold plus bold space bold QR over denominator bold DE bold space bold plus bold space bold DF end fraction bold space bold space bold space bold space bold space bold space bold space bold space bold. bold. bold. bold space bold left parenthesis bold 2 bold right parenthesis bold space$

(1) અને (2) પરથી,

$fraction numerator bold PQ bold space bold plus bold space bold QR over denominator bold DE bold space bold plus bold space bold DF end fraction bold space bold equals bold space bold PR over bold EF bold therefore bold space bold 15 over bold 10 bold space bold equals bold space bold 6 over bold EF bold therefore bold space bold EF bold space bold equals bold space bold 6 bold space bold cross times bold space bold 10 over bold 15 bold therefore bold space bold EF bold space bold equals bold space bold 4 bold space$