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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 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.

$bold increment bold space bold PQR$ અને $bold increment bold space bold XYZ$ માટે સંગતતા $bold PQR bold space bold left right arrow bold space bold YZX bold space$ સમરૂપતા છે.

$bold therefore bold space bold m bold space bold angle bold P bold space bold equals bold space bold m bold space bold angle bold Y bold space$ અને $bold m bold space bold angle bold Q bold space bold equals bold space bold m bold space bold angle bold Z$

હવે, $bold m bold angle bold P bold space bold space bold equals bold space bold 2 bold m bold space bold angle bold Q$
$bold therefore bold space bold m bold angle bold Y bold space bold equals bold space bold 2 bold m bold angle bold Z bold therefore bold m bold angle bold Z bold space bold equals bold space bold 1 over bold 2 bold space bold m bold space bold angle bold Y bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold. bold. bold. bold space bold left parenthesis bold 1 bold right parenthesis$

$bold increment bold space bold XYZ$ માં, $bold m bold angle bold X bold space bold plus bold space bold m bold space bold angle bold Y bold space bold plus bold space bold m bold space bold angle bold Z bold space bold equals bold space bold 180 bold space$

$bold therefore bold space bold 120 bold space bold plus bold space bold m bold angle bold Y bold space bold plus bold space bold 1 over bold 2 bold space bold m bold space bold angle bold Y bold space bold equals bold space bold 180 bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold space bold left square bracket bold space bold because bold space bold m bold space bold angle bold space bold X bold space bold equals bold space bold 120 bold space bold અન ે bold space bold left parenthesis bold 1 bold right parenthesis bold space bold right square bracket bold space bold therefore bold space bold 3 over bold 2 bold space bold m bold space bold angle bold Y bold space bold equals bold space bold 60 bold space bold therefore bold space bold m bold space bold angle bold Y bold space bold equals bold space bold 60 bold space bold cross times bold space begin inline style bold 2 over bold 3 end style bold therefore bold space bold m bold space bold angle bold Y bold space bold equals bold space bold 40 bold space bold space$