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CBSE Gujarat Board Haryana Board

Previous Year Papers

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Currently only available for
Class 10 Class 12

સમરૂપતા અને પાયથાગોરસ પ્રમેય

bold increment bold space bold ABC

માં

bold angle bold B

કાટકોણ છે.

top enclose bold BD

bold perpendicular bold space top enclose bold AC

અને

bold D bold space bold element of bold space top enclose bold AC bold space bold.

જો

bold AD bold space bold equals bold space bold 4 bold DC

તો સાબિત કરો કે

bold BD bold space bold equals bold space bold 2 bold DC bold.

પક્ષ :

$bold increment bold space bold ABC$ માં $bold angle bold B$ કાટકોણ છે. $top enclose bold BD bold space bold perpendicular bold space top enclose bold AC$ અને $bold D bold space bold element of bold space top enclose bold AC$ તથા $bold AD bold space bold equals bold space bold 4 bold DC$
સાધ્ય :

$bold BD bold space bold equals bold space bold 2 bold DC$

સાબિતી :

$bold increment bold space bold ABC bold space$ માં $bold angle bold B$ કાટકોણ છે. $top enclose bold BD bold space bold perpendicular bold space top enclose bold AC$ અને $bold D bold space bold element of bold space top enclose bold AC bold.$

$bold therefore bold space bold BD to the power of bold 2 bold space bold equals bold space bold AD bold space bold times bold space bold DC bold space$ ( $bold because$ ઉપપ્રમેય)

$bold therefore bold space bold BD to the power of bold 2 bold space bold equals bold space bold 4 bold DC bold space$ ( $bold because$ પક્ષ)

$bold therefore bold space bold BD to the power of bold 2 bold space bold equals bold space bold 4 bold space bold times bold space bold DC to the power of bold 2 bold space bold therefore bold space bold BD bold space bold equals bold space bold 2 bold DC$

એક ત્રિકોણની બાજુઓનાં માપ 5, 12 અને 13 છે. સાબિત કરો કે ત્રિકોણ કાટકોણ ત્રિકોણ છે. ત્રિકોણના કર્ણ પરના વેધની લંબાઇ શોધો.

bold increment bold space bold PQR

માં

top enclose bold QM

એ કર્ણ

top enclose bold PR

પરનો વેધ છે. જો

bold PM bold space bold equals bold space bold 8 bold comma bold space bold RM bold space bold equals bold space bold 12 bold space

હોય, તો

bold PQ bold comma bold space bold QR

અને

bold QM

શોધો.

bold increment bold space bold ABC bold space

માં

bold m bold space bold angle bold space bold B bold space bold equals bold space bold 90 bold degree bold comma bold space top enclose bold BM bold space bold perpendicular bold space top enclose bold AC bold comma bold space bold M bold space bold element of bold space top enclose bold AC bold space bold. bold space

જો $bold AM bold space bold minus bold space bold MC bold space bold space bold equals bold space bold 7 bold comma bold space bold AB to the power of bold 2 bold space bold minus bold space bold AC to the power of bold 2 bold space bold equals bold space bold 175 bold space$ હોય, તો AC શોધો.