Question

line segment AB and CD bisects at O. Join AC and BD. prove that triangle AOC congruent to triangle BOD

Answer 1

You can say that segment AO is congruent to OB and CO is congruent to OD because the line segments AB and CD are bisected, or cut in half. 

Then you can say that angle BOD and angle AOC are congruent because they are vertical angles. Essentially you are proving this through SAS.

Hope this helps