There is something wrong with this definition for a pair of vertical angles: "If line AB and line CD intersect at point P, then angle APC and angle BPD are a pair of vertical angles.
What is wrong??!?
Point D and Point C could lie on the same end of the line so that both points are on one side of the intersection point (point P)
Well, the only thing I can see "lacking" in the definition is if the intersection P is actually also one of the A,B,C,D points. So you could just say ""If line AB and line CD intersect at point P such that P is different from A, B, C or D, then angle APC and angle BPD are a pair of vertical angles."
It doesn't say that the angles are congruent.
The given definition for vertical angles is incorrect. A pair of vertical angles is formed when two lines intersect, creating four angles. In this case, if line AB and line CD intersect at point P, then angle APC and angle BPD are not a pair of vertical angles.
To correct the definition, we need to understand the properties of vertical angles. Vertical angles are a pair of non-adjacent angles formed by two intersecting lines. The two pairs of vertical angles are always congruent, meaning they have equal measures. This means that if angle APC and angle BPD are vertical angles, then their measures must be equal.
Therefore, the correct definition for a pair of vertical angles would be: "If line AB and line CD intersect at point P, then angle APC and angle BPD are a pair of vertical angles if and only if angle APC is congruent to angle BPD."