Question

如图,已知四边形ABCD中,E,F是DC的边三等分点,G,H是AB的三等分点 求证：S四边形GHFE=1/3 S四边形A

Answer 1

∵AG=GH=HB,DE=EF=FC,

∴SΔACE=2/3SΔADC,SΔACH=2/3SΔABC,

∴SΔACE+SΔACH=2/3(SΔADC+SΔABC)=2/3S四边形ABCD=2/3S,

即S四边形AECH=2/3S,

∵SΔEGH=1/2SΔEAH,SΔHEF=1/2SΔHEC,

∴SΔEGH+SΔHEF=1/2*S四边形AECF=1/3S,

即S四边形GHFE=1/3S.