Answer :

Final Answer:

ED must be parallel to AC, and ED must equal half the length of AC.

Explanation:

When a line is added to connect points E and D in a geometric figure, it is essential to analyze the properties of the figure to determine the relationship between ED, AC, and the length of ED.

In this case, it is stated that ED bisects both AB and BC. When a line bisects a line segment, it means that it divides the segment into two equal parts. Therefore, ED divides both AB and BC into two equal lengths. This implies that the length of ED must be equal to half the length of both AB and BC.

Now, for ED to be parallel to AC, we can apply the transversal property. If ED bisects both AB and BC, it divides the interior angles at E and D into two equal angles. According to the corresponding angles postulate, these pairs of angles are congruent. Therefore, angle EDA is congruent to angle CDE, and angle AED is congruent to angle EDC, indicating that ED is parallel to AC.

So, in summary, ED is parallel to AC because it bisects the two line segments AB and BC, and the length of ED is equal to half the length of AC.

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