Triangle A C B is cut by line segment E D. Line segment E D goes from side B C to side A C. The length of B A is 4 x minus 6 and the length of E D is x 2. The length of B E is x. Sides B E and E C are congruent. Sides A D and D C are congruent. What is the length of BC? From the markings on the diagram, we can tell E is the midpoint of BC and is the midpoint of AC We can apply the theorem: ED = One-halfBA. Substituting in the expressions for the lengths and solving for x, we get x =. Now, since BE = x, then BC =.