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a: Ta có: \(AE=\frac23\times AD\)
=>\(S_{ABE}=\frac23\times S_{ABD}\)
Ta có: \(BD=\frac13\times BC\)
=>\(S_{ABD}=\frac13\times S_{ABC}\)
=>\(S_{ABE}=\frac23\times\frac13\times S_{ABC}=\frac29\times S_{ABC}\) (1)
ta có: \(S_{ABD}+S_{ACD}=S_{ABC}\)
=>\(S_{ACD}=S_{ABC}-S_{ABD}=S_{ABC}-\frac13\times S_{ABC}=\frac23\times S_{ABC}\)
Ta có: AE+ED=AD
=>\(ED=AD-AE=AD-\frac23\times AD=\frac13\times AD\)
=>\(S_{EDC}=\frac13\times S_{ADC}=\frac13\times\frac23\times S_{ABC}=\frac29\times S_{ABC}\) (2)
Từ (1),(2) suy ra \(S_{ABE}=S_{EDC}\)
b: Ta có: \(DE=\frac13\times DA\)
=>\(S_{BED}=\frac13\times S_{ABD}=\frac13\times\frac13\times S_{ABC}=\frac19\times S_{ABC}\)
Ta có: \(AE=\frac23\times AD\)
=>\(S_{AEC}=\frac23\times S_{ADC}=\frac23\times\frac23\times S_{ABC}=\frac49\times S_{ABC}\)
=>\(\frac{S_{BED}}{S_{AEC}}=\frac{\frac19}{\frac49}=\frac19\times\frac94=\frac14\)
a: Ta có: \(BD+DC=BC\)
=>\(DC=BC-BD=BC-\frac13\times BC=\frac23\times BC\)
=>\(S_{ADC}=\frac23\times S_{ABC}\)
Ta có: \(BD=\frac13\times BC\)
=>\(S_{ABD}=\frac13\times S_{ABC}\)
AE+ED=AD
=>\(ED=AD-AE=AD-\frac23\times AD=\frac13\times AD\)
=>\(S_{EDC}=\frac13\times S_{ADC}=\frac13\times\frac23\times S_{ABC}=\frac29\times S_{ABC}\)
Ta có: \(AE=\frac23\times AD\)
=>\(S_{ABE}=\frac23\times S_{ABD}=\frac23\times\frac13\times S_{ABC}=\frac29\times S_{ABC}\)
Do đó: \(S_{EDC}=S_{ABE}\)
b: Ta có: \(DE=\frac13\times DA\)
=>\(S_{BED}=\frac13\times S_{ABD}=\frac13\times\frac13\times S_{ABC}=\frac19\times S_{ABC}\)
Ta có: \(AE=\frac23\times AC\)
=>\(S_{AEC}=\frac23\times S_{ADC}=\frac23\times\frac23\times S_{ABC}=\frac49\times S_{ABC}\)
=>\(\frac{S_{BED}}{S_{AEC}}=\frac19:\frac49=\frac14\)
a: S ABE=S EBD=1/2*S ABD
DC=1/2DB
nên S ADC=1/2*S ABD
=>S ABE=S EBD=S ADC
b: S ABC=3/2*24=36cm2