चित्र में `DE||BC ` तथा AD : DB = 5 :4 हो, तो ` (ar (Delta DEF))/(ar(Delta CFB))` ज्ञात करो|

Explanation

दिया है: `Delta ABC ` में
` " "DE ||BC `
`rArr " "angle ADE =angle ABC` तथा ` angle AED =angle ACB " " ` [संगत कोण]
अतः ` Delta ADE ` तथा ` Delta ABC ` में
` " "angle A =angle A " " ` [उभयनिष्ट कोण]
` " "angle ADE =angle ABC `
तथा ` " "angle AED =angle ACB `
` therefore " "Delta AED ~ Delta ABC `
` rArr " "(AD)/(AB)=(DE)/(BC) " " ` [समरूपता की AAA कसौटी से]
`rArr " "(AD)/(AB)= (DE)/(BC) " "...(i)`
दिया है| `" " (AD)/(DB)= (5)/(4)`
`rArr " "(DB)/(AD) =(4)/(5)`
` rArr" "(DB)/(AD) +1 =(4)/(5) +1 `
` rArr " "(DB+ AD)/( AD) =(9)/(5)`
` rArr " "(AB)/( AD) = ( 9)/(5) rArr (AD)/(AB) =(5)/(9) `
` therefore " "(DE)/( BC) =(5)/(9) " "[ because (AD)/ (AB) =(DE)/( BC) (i) ` से ]
` Delta DFE ` और ` Delta CFB` में
`" "angle 1 =angle 3" " ` [एकांतर अतः कोण]
तथा ` " "angle 2 =angle 4 " " ` [शीर्षाभिमुख कोण ]
अतः समरूपता की AA कसौटी से
` " "Delta DFE ~ Delta CFB `
` rArr " "(ar(Delta DFE))/( ar (Delta CFB) ) =(DE^(2))/( BC^(2))`
`rArr " "(ar(Delta DFE))/( ar (Delta CFB) ) = ( (5)/(9))^(2) =( 25)/( 81) " " ` [(i ) से ]