In the given diagram, we are told that AB and CD are parallel, and that BC and DG are also parallel. We want to prove that AB * CG is equal to CD* AC. As a first step, let's show that △ ABC and △ CDG are similar triangles.
Note that A, C, and G are on a straight line, and AB ∥ CD. Moreover, ∠ BAC and ∠ DCG are corresponding angles. Therefore, by the Corresponding Angles Theorem, these two angles are congruent.
Similarly, it is also given that BC is parallel to DG. By the same theorem as before, ∠ BCA and ∠ DGC are also congruent angles.
We now know that two angles of triangle △ ABC are congruent to two angles of triangle △ CDG.
By the Angle-Angle Similarity Postulate, this means that triangles △ ABC and △ CDG are similar.
△ ABC~ △ CDG
In similar triangles corresponding sides are proportional. Note that AB and CD are corresponding sides, and AC and CG are also corresponding sides. Let's write a proportion using the lengths of these sides.
AB:CD=AC:CG
We will write the above ratios as fractions, and rewrite the equation.
