Here's the figure:

Given that line AX is congruent to line DX, and line XB is congruent to line XB:

Prove that line AC is congruent to line BD. Code:

Statements Reasons
1. Line Ax is congruent to Dx 1. Given
2. <AXD is congruent to <BXC 2. Vertical Angles Theorem
3. X is the midpoint of line AC 3. Definition of a Midpoint
and line BD.
4. Line AC is congruent to line BD. 4. Definition of a Midpoint

This is my try, I really don't think it's correct, so if somebody could help me out that would be cool.