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ગણિત ધોરણ 9 દ્વિતીય સત્ર

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bold square bold space bold ABCD માં જો bold m bold space bold angle bold space bold A bold space bold equals bold space bold m bold space bold angle bold space bold B bold space bold equals bold space bold 70 bold comma bold space bold m bold space bold angle bold space bold C bold space bold equals bold space bold 100 હોય, તો bold m bold space bold angle bold space bold D શોધો.





bold square bold space bold ABCDમ ાં bold comma bold space bold m bold space bold angle bold space bold A bold space bold plus bold space bold m bold space bold angle bold space bold B bold space bold plus bold space bold m bold space bold angle bold space bold C bold space bold plus bold space bold m bold space bold angle bold space bold D bold space bold equals bold space bold 360

bold therefore bold space bold 70 bold space bold plus bold space bold 70 bold space bold plus bold space bold 100 bold space bold plus bold space bold m bold space bold angle bold space bold D bold space bold equals bold space bold 360

bold therefore bold space bold 240 bold space bold plus bold space bold m bold space bold angle bold space bold D bold space bold equals bold space bold 360

bold therefore bold space bold m bold space bold angle bold space bold D bold space bold equals bold space bold 360 bold space bold minus bold space bold 240

bold therefore bold space bold m bold space bold angle bold space bold D bold space bold equals bold space bold 120

આપેલી આકૃતિમાં દર્શાવેલ bold square bold space bold XYZW ના સંદર્ભમાં નીચેની માહિતી આપો :


(1) બાજુઓ
(2) ખૂણાઓ
(3) વિકર્ણોના નામ
(4) પાસપાસેની બાજુઓનાં નામ
(5) સામસામેની બાજુઓનાં નામ
(6) પાસપાસેના ખૂણાઓનાં નામ
(7) સામસામેના ખૂણાઓનાં નામ
open parentheses bold 8 close parentheses bold space bold XW with bold bar on top bold space bold intersection bold space bold YZ with bold bar on top

open parentheses bold 9 close parentheses bold space bold YX with bold bar on top bold space bold intersection bold space bold XW with bold left right arrow on top


(1) bold square bold space bold XYZW ની બાજુઓ bold XY with bold bar on top bold comma bold space bold YZ with bold bar on top bold comma bold space bold ZW with bold bar on top bold space bold અન ે bold space bold WX with bold bar on top છે.

(2) bold square bold space bold XYZW ના ખૂણાઓ bold angle bold space bold X bold comma bold space bold angle bold space bold Y bold comma bold space bold angle bold space bold Z bold space bold અન ે bold space bold angle bold space bold W છે.

(3) bold square bold space bold XYZW ના વિકર્ણો bold XZ with bold bar on top bold space bold અન ે bold space bold YW with bold bar on top  છે.

(4) bold square bold space bold XYZW માં પાસપાસેની બાજુઓ નીચે પ્રમાણે છે :

open parentheses bold i close parentheses bold space bold XY with bold bar on top bold space bold અન ે bold space bold YZ with bold bar on top

bold left parenthesis bold ii bold right parenthesis bold space bold YZ with bold bar on top bold space bold અન ે bold space bold ZW with bold bar on top

bold left parenthesis bold iii bold right parenthesis bold space bold ZW with bold bar on top bold space bold અન ે bold space bold WX with bold bar on top

bold left parenthesis bold iv bold right parenthesis bold space bold WX with bold bar on top bold space bold અન ે bold space bold XY with bold bar on top


(5) bold square bold space bold XYZW માં સામસામેની બાજુઓ નીચે પ્રમાણે છે :

open parentheses bold i close parentheses bold space bold XY with bold bar on top bold space bold અન ે bold space bold ZW with bold bar on top

open parentheses bold ii close parentheses bold space bold YZ with bold bar on top bold space bold અન ે bold space bold WX with bold bar on top


(6) bold square bold space bold XYZW માં પાસપાસેના ખૂણાઓ નીચે પ્રમાણે છે :

open parentheses bold i close parentheses bold space bold angle bold space bold X bold space bold અન ે bold space bold angle bold space bold Y

open parentheses bold ii close parentheses bold space bold angle bold space bold Y bold space bold અન ે bold space bold angle bold space bold Z

open parentheses bold iii close parentheses bold space bold angle bold space bold Z bold space bold અન ે bold space bold angle bold space bold W

open parentheses bold iv close parentheses bold space bold angle bold space bold W bold space bold અન ે bold space bold angle bold space bold X


(7) bold square bold space bold XYZW માં પાસપાસેના ખૂણાઓ નીચે પ્રમાણે છે :

open parentheses bold i close parentheses bold space bold angle bold space bold X bold space bold અન ે bold space bold angle bold space bold Z

open parentheses bold ii close parentheses bold space bold angle bold space bold Y bold space bold અન ે bold space bold angle bold space bold W


open parentheses bold 8 close parentheses bold space bold XW with bold bar on top bold space bold intersection bold space bold YZ with bold bar on top bold space bold equals bold space bold empty set

bold left parenthesis bold 9 bold right parenthesis bold space bold YX with bold bar on top bold space bold intersection bold space bold XW with bold left right arrow on top bold space bold equals bold space open curly brackets bold X close curly brackets


bold square bold space bold PQRSમાં જો bold m bold space bold angle bold space bold P bold space bold equals bold space bold 2 bold x bold comma bold space bold m bold space bold angle bold space bold Q bold space bold equals bold space bold 3 bold x bold comma bold space bold m bold space bold angle bold space bold R bold space bold equals bold space bold 4 bold x bold space bold અન ે bold comma bold space bold m bold space bold angle bold space bold S bold space bold equals bold space bold 6 bold x bold comma bold space bold ત ો bold space bold square bold space bold PQRS ના દરેક ખૂણાનુ માપ શોધો.




bold square bold space bold PQRSમ ાં bold comma bold space bold m bold space bold angle bold space bold P bold space bold plus bold space bold m bold space bold angle bold space bold Q bold space bold plus bold space bold m bold space bold angle bold space bold R bold space bold plus bold space bold m bold space bold angle bold space bold S bold space bold equals bold space bold 360

bold therefore bold space bold 2 bold x bold space bold plus bold space bold 3 bold x bold space bold plus bold space bold 4 bold x bold space bold plus bold space bold 6 bold x bold space bold equals bold space bold 360

bold therefore bold space bold 15 bold x bold space bold equals bold space bold 360

bold therefore bold space bold x bold space bold equals bold space bold 360 over bold 15

bold therefore bold space bold x bold space bold equals bold space bold 24

bold હવ ે bold comma bold space

bold m bold space bold angle bold space bold P bold space bold equals bold space bold 2 bold x bold space bold equals bold space bold 2 bold space bold cross times bold space bold 24 bold space bold equals bold space bold 48

bold m bold space bold angle bold space bold Q bold space bold equals bold space bold 3 bold x bold space bold equals bold space bold 3 bold space bold cross times bold space bold 24 bold space bold equals bold space bold 72

bold m bold space bold angle bold space bold R bold space bold equals bold space bold 4 bold x bold space bold equals bold space bold 4 bold space bold cross times bold space bold 24 bold space bold equals bold space bold 96

bold m bold space bold angle bold space bold S bold space bold equals bold space bold 6 bold x bold space bold equals bold space bold 6 bold space bold cross times bold space bold 24 bold space bold equals bold space bold 144

bold square bold space bold ABCDમાં bold angle bold space bold A bold comma bold space bold angle bold space bold B bold comma bold space bold angle bold space bold C bold space bold અન ે bold space bold angle bold space bold D નાં માપ 2 : 5 : 6 : 7ના પ્રમાણમાં હોય, તો bold square bold space bold ABCDના દરેક ખૂણાનું માપ શોધો.


bold square bold space bold ABCDમ ાં bold comma bold space bold m bold space bold angle bold space bold A bold space bold colon bold space bold m bold space bold angle bold space bold B bold space bold colon bold space bold m bold space bold angle bold space bold C bold space bold colon bold space bold m bold space bold angle bold space bold D bold space bold equals bold space bold 2 bold space bold colon bold space bold 5 bold space bold colon bold space bold 6 bold space bold colon bold space bold 7

bold જ ો bold comma bold space bold m bold space bold angle bold space bold A bold space bold equals bold space bold 2 bold x bold comma bold space bold ત ો bold space bold m bold space bold angle bold space bold B bold space bold equals bold space bold 5 bold x bold comma bold space bold m bold space bold angle bold space bold C bold space bold equals bold space bold 6 bold x bold space bold અન ે bold space bold m bold space bold angle bold space bold D bold space bold equals bold space bold 7 bold x

bold હવ ે bold comma bold space bold square bold space bold ABCDમ ાં bold comma bold space bold m bold space bold angle bold space bold A bold space bold plus bold space bold m bold space bold angle bold space bold B bold space bold plus bold space bold m bold space bold angle bold space bold C bold space bold plus bold space bold m bold space bold angle bold space bold D bold space bold equals bold space bold 360

bold therefore bold space bold 2 bold x bold space bold plus bold space bold 5 bold x bold space bold plus bold space bold 6 bold x bold space bold plus bold space bold 7 bold x bold space bold equals bold space bold 360

bold therefore bold space bold 20 bold x bold space bold equals bold space bold 360

bold therefore bold space bold x bold space bold equals bold space bold 360 over bold 20

bold therefore bold space bold x bold space bold equals bold space bold 18

bold હવ ે bold comma bold space bold m bold space bold angle bold space bold A bold space bold equals bold 2 bold x bold space bold equals bold space bold 2 bold space bold cross times bold space bold 18 bold space bold equals bold space bold 36

bold m bold space bold angle bold space bold B bold space bold equals bold space bold 5 bold x bold space bold equals bold space bold 5 bold space bold cross times bold space bold 18 bold space bold equals bold space bold 90

bold m bold space bold angle bold space bold C bold space bold equals bold space bold 6 bold x bold space bold equals bold space bold 6 bold space bold cross times bold space bold 18 bold space bold equals bold space bold 108

bold m bold space bold angle bold space bold D bold space bold equals bold space bold 7 bold x bold space bold equals bold space bold 7 bold space bold cross times bold space bold 18 bold space bold equals bold space bold 126


bold square bold space bold PQRS bold space bold equals bold space bold square bold space bold PSQR છે ? કારણ આપો.

ના, bold square bold space bold PQRS bold space bold not equal to bold space bold square bold space bold PSQR

કારણ : bold square bold space bold PQRS ના વિકર્ણો bold PR with bold bar on top bold space bold અન ે bold space bold QS with bold bar on top છે, જ્યારે bold square bold space bold PSQR ના વિકર્ણો bold PQ with bold bar on top bold space bold અન ે bold space bold SR with bold bar on top છે.

આમ, bold square bold space bold PQRS bold space bold અન ે bold space bold square bold space bold PSQR ના વિકર્ણો સમાન નથી.