Final answer:
To prove that triangles are similar by the SAS similarity theorem, one must show that one pair of angles is congruent and the sides including these angles are in proportion, specifically that AC/GI = BC/HI.
Step-by-step explanation:
To prove that two triangles are similar by the SAS (Side-Angle-Side) similarity theorem, it needs to be shown that one angle of the first triangle is congruent to one angle of the second triangle, and the sides that include these angles are in proportion. Since the question provides pairs of angles labeled with 'C' and 'G' and sides labeled as 'AC', 'GI', 'HI', and 'BC', the correct relationship to prove similarity by SAS is:
AC/GI = BC/HI
It is important to have the corresponding sides in proportion, which are the sides around the congruent angles in each triangle. The proportion shows that the lengths of the sides of the first triangle are in the same ratio to the corresponding sides of the second triangle, which is a requirement for SAS similarity.