4. Triangle ABC is similar to triangle DEF. Which proportion must be true? Options: a. AB/BC = FE/DE, b. AC/DF = AB/FE, c. BC/EF = FD/CA, d. AC/CB = DF/FE

Answer

To determine which proportion must be true for similar triangles ABC and DEF, we match corresponding sides. In similar triangles, corresponding sides are proportional. Looking at the triangles, vertex A corresponds to vertex D, vertex B corresponds to vertex F, and vertex C corresponds to vertex E. Therefore, the corresponding sides are AB and DF, BC and FE, and CA and ED. Let's check option d: AC/CB = DF/FE. AC corresponds to DF, and CB corresponds to FE. Setting them as a ratio gives AC/CB = DF/FE, which correctly maintains the ratio of sides within triangle ABC to the corresponding sides in triangle DEF. Therefore, option d is the correct proportion.