Geometry problems help?

Question

If CA=AT, then A is the midpoint of segment CT.

If point A is not the midpoint of segment CT, then CA cannot equal AT.

There is something wrong with this definition for a pair or vertical angles. If line AB and CD intersect at point P, then angle APC and angel BPD are a pair or vertical angles. Show why this is not correct.

All these are false, and I have answers. I need to know if they're right or not.

Answer 1

1) For the midpoint portion, the statement is true. The definition of "midpoint" is that the point is exactly midway between the two other points. "Exactly midway" means the measure from that point to either of the other two points is the same.

2) For a "pair or vertical angles"? I have to assume you mean "pair of vertex angles." This statement is false only in the first sentence where it says "There is something wrong..." That is because this IS the definition of vertex angles and so nothing is actually wrong with the statement except saying it is wrong.