a: \(S_{ABC}=\dfrac{1}{2}\cdot AE\cdot BC\)
\(S_{ADC}=\dfrac{1}{2}\cdot AF\cdot DC\)
\(S_{ABC}=S_{ADC}\left(\Delta ABC=\Delta ADC\right)\)
nên AE*BC=AF*DC
=>AE/AF=DC/BC=AB/AD=AB/BC
b: \(S_{AMCN}=S_{ABCD}-\left(S_{DCN}+S_{BMC}\right)\)
\(=S_{ABCD}-\dfrac{1}{2}\cdot S_{ADC}-\dfrac{1}{2}\cdot S_{ABC}\)
\(=S_{ABCD}-\dfrac{1}{4}\cdot S_{ABCD}-\dfrac{1}{4}\cdot S_{ABCD}\)
\(=\dfrac{1}{2}\cdot S_{ABCD}\)
=>\(S_{ABCD}=2\cdot S_{AMCN}\)
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