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

When two triangles are similar, such as triangle ABC and triangle DEF, the corresponding sides are proportional in the same order. Let us check the given options based on the similarity. Triangle ABC corresponds to triangle DEF, meaning vertex A corresponds to D, vertex B to E, and vertex C to F. Thus, the corresponding sides are AB and DE, BC and EF, and AC and DF. Let us examine option c: BC/EF = CA/FD. In option c, it is written as BC/EF = FD/CA, which is the reciprocal or can be rewritten correctly. Let us look at option d: AC/CB = DF/FE. This means AC (side 1-3) over CB (side 3-2) equals DF (side 1-3) over FE (side 3-2). This maintains the correct correspondence of sides between the two triangles. Therefore, option d is correct.