如图所示,在△ABC和△CAD中,DA∥BC,CD交AB于E,且AE:EB=1:2,EF∥BC交AC于F,S△ADE=1,求S△AEF和S△BCE.

问题描述:

如图所示,在△ABC和△CAD中,DA∥BC,CD交AB于E,且AE:EB=1:2,EF∥BC交AC于F,S△ADE=1,求S△AEF和S△BCE

∵DA∥BC,∴△ADE∽△BCE.∴S△ADE:S△BCE=AE2:BE2.∵AE:BE=1:2,∴S△ADE:S△BCE=1:4.∵S△ADE=1,∴S△BCE=4.∵S△ABC:S△BCE=AB:BE=3:2,∴S△ABC=6.∵EF∥BC,∴△AEF∽△ABC.∵AE:AB=1:3,∴...