In the figure above, is a parallelogram. Point lies on . cuts diagonal at and is extended to meet the extension of at . If and , find .
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△ F D G and △ A B G are similar triangles,
∴ G A G F = G B G D
△ B G E and △ A G D are similar triangles,
∴ G B G D = G E G A
We equate G B G D = G B G D , we have
G A G F = G E G A
Substituting, we get
6 4 + E F = 4 6
4 + E F = 4 3 6
4 + E F = 9
E F = 9 − 4
E F = 5 answer