toán 9 . bài tập cần giải gấp

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duonghongsonmeo

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M

microwavest

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Ta có: $\Delta{AEB} \sim \Delta{AFD}$ (g-g):

\Rightarrow $\dfrac{AB}{DF}=\dfrac{AE}{AF}$ \Leftrightarrow $\dfrac{AB}{AE}=\dfrac{DF}{AF}$ \Leftrightarrow $\dfrac{AB^2}{AE^2}=\dfrac{DF^2}{AF^2}$

mà: $\dfrac{DF^2}{AF^2} + \dfrac{AB^2}{AF^2} = \dfrac{DF^2+AD^2}{AF^2} = 1$

\Rightarrow $\dfrac{AB^2}{AE^2}+ \dfrac{AB^2}{AF^2} = 1$ \Leftrightarrow $\dfrac{1}{AE^2} + \dfrac{1}{AF^2} = \dfrac{1}{AB^2}$
 
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