Answer
We use figure 6.51. In order to do this proof, we must prove that triangles ART and ABC are similar. Both triangles share point A, which is congruent to itself by the identity property. In addition, since BC and RT are parallel, we obtain that the two sets of angles (R and T as well as B and C) are congruent. Thus, it follows that the triangles are similar, so we can create a proportion:
$\frac{AT}{AR} =\frac{AB}{AC} \\AT \cdot AC =AB \cdot AR$
