Final answer:
To prove triangle AEC is congruent to triangle BED, we utilize given data on line segments and midpoints. Therefore, the correct answer is (d) Not enough information to determine.
Step-by-step explanation:
To prove that triangle AEC is congruent to triangle BED, given that E is the midpoint of AB and CD and that AC is congruent to BD, we need to examine the information provided and determine which congruence criterion can be used. First, since E is the midpoint of both segments AB and CD, we can deduce that AE = EB and CE = DE by the definition of a midpoint, which divides a line segment into two equal parts. Next, we know that AC is congruent to BD from the given information, meaning that AC = BD. However, since E is the midpoint of CD and AC is congruent to BD, we also have CE = DE. Therefore, the correct answer is (d) Not enough information to determine.