Final answer:
To prove midsegment overline{DE} is parallel to overline{AC} and that DE is half the length of AC, we apply the Triangle Midsegment Theorem to show that overline{DE} must be parallel and measure half the length of side overline{AC} in ABC.
Step-by-step explanation:
To show that midsegment overline{DE} is parallel to overline{AC} using the graph of △ ABC, we must consider the properties of triangles and the definition of a midsegment. A midsegment in a triangle is a segment that connects the midpoints of two sides of the triangle.
By the Triangle Midsegment Theorem, the midsegment is parallel to the third side of the triangle and is half the length of that side.
So, if D and E are the midpoints of the sides AB and BC, respectively, in △ ABC, then by definition, overline{DE} is a midsegment. As per the theorem, overline{DE} must be parallel to overline{AC}, and its length DE should be exactly half the length of AC. This can be expressed mathematically as DE = frac{1}{2}AC.
To prove these relationships, we would need to measure the lengths of overline{AC} and overline{DE} from the graph and check that DE is indeed half the length of AC.
Additionally, checking the angles made by overline{DE} with either overline{AB} or overline{BC}, where they should show that overline{DE} creates corresponding angles that are congruent with those formed by overline{AC}, would confirm the parallel nature of these segments.