Proportions Within Each Figure

In algebra, you can cross-multiply in a proportion such as , getting ad = bc.  Another proportion that gives the same cross-product is .  When interpreted for similar triangles, this shows that if you take the ratio of two sides in one triangle and the ratio of the two corresponding sides in the other, then these ratios will be the same.

For example,  and the following ratios are all equal:

 

In other words, .

This is another way to express SSS similarity.  That is, if all three corresponding ratios are the same, then the triangles are similar.