Explanation:
The vertical angles are congruent. The right angles are congruent. There are 2 angles of a triangle congruent to 2 angles of anther triangle. By AA Similarity the triangles are similar.
Statement A. (vertical angles are congruent)
Statement D. (right angles are congruent)
Triangle AEC is similar to triangle BDC.
Statement E is true but does not help.
Correct statement of proportional side lengths:
BD/AE = CD/CE
x/150 = 200/50
x/150 = 4
x = 600
P.S. I think there is a mistake in the problem. I don't think that statement E is correct. It is a true statement, but it is useless. Statement F is false.