Matching the Corners

Before you write a proportion, you need to know which side matches which. A similarity statement tells you in its order of letters. "Triangle ABC is similar to triangle DEF" means that A matches D, B matches E and C matches F. So side AB matches DE, BC matches EF and CA matches FD. Read the letters in pairs, and the matching sides follow.

Without a statement, use the angles. Matching sides face matching angles. The side opposite the largest angle in one triangle matches the side opposite the largest angle in the other. The same goes for the smallest angle. When a figure marks equal angles with arcs, the side across from a single arc in one triangle matches the side across from the single arc in the other. Find the matching sides first, and only then write the proportion.