In Fig. 1, $MN \parallel BC$ and $AM : MB = 1 : 2$, then $\frac{ ext{ar}( riangle AMN)}{ ext{ar}( riangle ABC)} = $ ________.

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Question

In Fig. 1, $MN \parallel BC$ and $AM : MB = 1 : 2$, then $\frac{	ext{ar}(	riangle AMN)}{	ext{ar}(	riangle ABC)} = $ ________.

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Accepted Answer

Step 1: Since $MN \parallel BC$, $	riangle AMN \sim 	riangle ABC$. $\frac{AM}{AB} = \frac{1}{3}$. $\frac{	ext{ar}(	riangle AMN)}{	ext{ar}(	riangle ABC)} = \left(\frac{1}{3}ight)^2 = \frac{1}{9}$

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