Final answer:
The nurse should identify that the goals have been met when the client reports weight gain, indicating that the hyperthyroidism is being effectively managed by propylthiouracil.
Step-by-step explanation:
The nurse should identify that the treatment goals for a client taking propylthiouracil have been met when the client reports weight gain. Propylthiouracil is a medication used to treat hyperthyroidism, a condition characterized by an overactive thyroid gland which leads to symptoms like weight loss, increased heart rate, and sweating. The goal of treatment with propylthiouracil is to reduce the overproduction of thyroid hormones and alleviate these symptoms. Thus, an increase in weight indicates a reduction in the symptoms of hyperthyroidism, signifying that the medication is effective.