\( A B C D \) is a parallelogram, \( G \) is the point on \( A B \) such that \( A G=2 G B, E \)...
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0\( A B C D \) is a parallelogram, \( G \) is the point on \( A B \) such that \( A G=2 G B, E \) is a point of \( D C \)
(W) such that \( C E=2 D E \) and \( F \) is the point of \( B C \) such that \( B F=2 F C \). Prove that:
(i) \( \operatorname{ar}(A D E G)=\operatorname{ar}(G B C E) \)
(ii) \( \operatorname{ar}(\triangle E G B)=\frac{1}{6} \operatorname{ar}(A B C D) \)
(iii) \( \operatorname{ar}(\triangle E F C)=\frac{1}{2} \operatorname{ar}(\triangle E B F) \)
(iv) \( \operatorname{ar}(\triangle E B G)=\operatorname{ar}(\triangle E F C) \)
(v) Find what portion of the area of parallelogram is the area of \( \triangle E F G \).
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