Geom Ch: Prove $AB=x^3$ Given $\triangle ABC$ & $\triangle AEF$

In summary, "Geom Ch" is a shortened way of saying "Geometry Chapter". In geometry, a proof is a logical argument that shows a statement to be true. Proving that AB = x^3 means finding evidence or using logical reasoning to show that the length of side AB in a triangle is equal to the cube of a number, x. In order to prove AB = x^3 in a triangle, we must have two triangles - triangle ABC and triangle AEF - and know that they are similar. We also need to know that the corresponding sides of the triangles, AB and AE, are in a ratio of x:1. Finally, we must have the knowledge that the ratio of the areas of the triangles is x^
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anemone
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The $\triangle ABC$ and $\triangle AEF$ are in the same plane. Between them, the following conditions hold:

1. The midpoint of $AB$ is $E$.
2. The points $A,\,G$ and $F$ are on the same line.
3. There is a point $C$ at which $BG$ and $EF$ intersect.
4. $CE=1$ and $AC=AE=FG$.

Prove that if $AG=x$, then $AB=x^3$.
 
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