All of the words listed - vigilant, precise, meticulous, particular - are synonyms that describe someone who pays close attention to detail and is careful in their actions. "Hasty" is the only word that does not fit this pattern, as it means to act quickly without careful consideration. Therefore, "hasty" could not be included in the list of words that are alike in meaning.
The word "particular" refers to something specific or distinct. Similarly, the word "specific" also means precise or detailed. Therefore, "specific" is the most similar in meaning to "particular".
The word "sad" refers to a feeling of unhappiness or sorrow. Therefore, the word "unhappy" is the most similar in meaning to "sad". The other options, such as "happy", "tears", and "cry", do not convey the same sense of sadness.
The two statements that together prove that Kelly has brown hair are "Rachael has brown hair" and "Kelly's hair is the same color as Rachael's." Since Rachael has brown hair and Kelly's hair is the same color as Rachael's, it can be inferred that Kelly also has brown hair.