Based only on the given information, it is guaranteed that AD = DB. FALSE
Determining the validity of the equation
From the given information:
Triangle ABC is mentioned.
Line CD divides line AB into two parts.
AB is perpendicular to CD.
Angle ACD is equivalent to angle BCD.
Given that AB is perpendicular to CD, and line CD divides line AB into two parts, forming right-angled triangles, it implies that CD is the height (or altitude) of triangle ABC with AB as the base. This means that the triangles formed by line CD are similar right-angled triangles.
If angle ACD is equivalent to angle BCD and both triangles are right-angled, it indicates that these triangles are similar (by angle-angle similarity criterion).
Regarding the statement "line AD equivalent to line DB," without further information on specific measurements or angles, it's not guaranteed based solely on the given information.
The information provided primarily suggests the similarity of the triangles and the equality of angles, not the specific equality of line segments AD and DB.
Therefore, the statement "line AD equivalent to line DB" cannot be concluded to be true based solely on the information given. The answer would be B. False.