Question

Susan notices that AC and DF are congruent in the image below. Which step could help her determine if _ABC _ _DEF by SAS?

Answer 1

 D due to SAS (Side Angle Side)... Though B and D may seem like the same thing, in congruence, if you have something like ΔABC ≅ ΔDEF. A matches with D, B matches with E, and C matches with F. Let's try B with this. "segment CA ≅ segment DF" C matches with F and A matches with D. So, the order matters. We have CA congruent to FD. Oops! This doesn't match due to the fact that it says DF instead of FD. However, D matches that. It also works, because you know that BC and EF are congruent and angles C and F are congruent. This makes sides congruent, then angles congruent in the middle, then sides congruent again. Hence Side Angle Side or SAS. A and C don't work, because they don't make AAS, SAS, or SSS. I hope that helps. :D