Final answer:
The most significant indicator of euglycemia in a child with diabetes mellitus is glycosylated hemoglobin (hemoglobin A1c), which reflects the average blood glucose level over the past 4 months.
Step-by-step explanation:
The most significant indicator of euglycemia, or normal blood glucose levels, in a child with diabetes mellitus is glycosylated hemoglobin (hemoglobin A1c). Hemoglobin A1c reflects the average blood glucose level over the past 4 months, giving a longer-term picture of blood glucose control. A level of hemoglobin A1c less than 7% is considered normal, while higher levels indicate poor control. Regular monitoring of hemoglobin A1c every 3 to 6 months is recommended in diabetes management.