document.write( "Question 981361: D and E ARE POINTS ON THE SIDES AB AND AC RESPECTIVELY OF TRIANGLE ABC SUCH THAT DE IS PARALLEL TO BC, AND AD:DB = 4:5. CD AND BE INTERSECT EACH OTHER AT F. FIND THE RATIO OF THE AREAS OF TRIANGLE DEF AND TRIANGLE BCF . \n" ); document.write( "
Algebra.Com's Answer #602489 by mananth(16946)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "DE || BC\r
\n" ); document.write( "\n" ); document.write( "AD/DB = AE/EF =4/5 ( Basic proportionality theorem)\r
\n" ); document.write( "\n" ); document.write( "In triangle ABE & ACD \r
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\n" ); document.write( "\n" ); document.write( "AD/DB = AE/EC and angle A is common\r
\n" ); document.write( "\n" ); document.write( "So triangles ABE & ACD are similar\r
\n" ); document.write( "\n" ); document.write( "Therefore AD/DB = EF/FB ( properties of similar triangles)
\n" ); document.write( "Similarly AE / EC = BF/FC\r
\n" ); document.write( "\n" ); document.write( "In Triangles AEF & BFC
\n" ); document.write( "angle FEC is congruent to angle BFE ( alternate angles)
\n" ); document.write( "angel DEF is = angle BFC ( vertically opposite angles)
\n" ); document.write( "Therefore they are similar\r
\n" ); document.write( "\n" ); document.write( "Area of triangle DFE / area of BFC = (4/5)^2 ( Properties of similar triangles\r
\n" ); document.write( "\n" ); document.write( "= 16/25\r
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