ANSWERS
Note: the answers that were correct have a check mark next to them.
EXPLANATION
As shown in the image, it is correct that AC = AC by the reflexive property.
Then, from the first two statements we can conclude that triangles ABC and CDA are congruent, by SSS:
Then, angles BCA and CAD are congruent because corresponding parts of congruent triangles re congruent (CPCTC).
If we draw the other diagonal as shown in the diagram, we can see that angles BEC and DEA are vertical angles and therefore they are congruent.
Then, we can conclude that triangles BCE and DAE are congruent by AAS:
We know that two consecutive angles and a non-included side are congruent to two consecutive angles and a non-included angle.
Then, segments BE and ED are congruent because CPCTC.
Finally, AC bisects BD by the angle bisector definition.
