Question

Line-segments AB and CD bisect each other at O. AC and BD are joined forming triangles AOC and BOD. State the three equality relations between the parts of the two triangles, that are given or otherwise known. Are the two triangles congruent? State in symbolic form. Which congruence condition do you use?

Answer 1

We have AO = OB and CO = OD since AB and CD bisect each other at O.

Also $\angle AOC=\angle BOD$ since they are opposite angles on the same vertex.
Therefore by SAS congruence condition, $△AOC\cong △BOD$.