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
a; Xét ΔAEB vuông tại E và ΔAFC vuông tại F có
\(\hat{EAB}\) chung
Do đó:ΔAEB~ΔAFC
=>\(\frac{AE}{AF}=\frac{AB}{AC}\)
=>\(\frac{AE}{AB}=\frac{AF}{AC}\)
=>\(AE\cdot AC=AF\cdot AB\)
b: Xét ΔAEF và ΔABC có
\(\frac{AE}{AB}=\frac{AF}{AC}\)
góc EAF chung
Do đó: ΔAEF~ΔABC
c: Xét ΔAEB vuông tại E có cos EAB=\(\frac{AE}{AB}\)
=>\(\frac{AE}{AB}=cos60=\frac12\)
ΔAEF~ΔABC
=>\(\frac{S_{AEF}}{S_{ABC}}=\left(\frac{AE}{AB}\right)^2=\left(\frac12\right)^2=\frac14\)
=>\(S_{ABC}=4\cdot S_{AEF}\)