Given AC = BC, prove AB = CD. Assume A, C, B, D are collinear in that order, and B is the midpoint of CD.

Here's the solution to the problem, based on a common interpretation for such geometry problems where points are collinear.

Given: $AC = BC$
To Prove: $AB = CD$

This problem requires an assumption about the arrangement of points A, B, C, D to be solvable. A common setup for such problems is that the points are collinear in a specific order, and additional relationships exist.

Assumption: The points A, C, B, D are collinear in that order, and B is the midpoint of segment CD. This means $CB = BD$.

Step 1: Use the given information $AC = BC$.
Since $AC = BC$, point C is the midpoint of segment AB. This implies that A, C, and B are collinear, and