To determine whether ab is the perpendicular bisector of cd at the intersection point p, we need to check the following properties:
- Perpendicularity: ab must be perpendicular to cd.
- Bisection: p must be the midpoint of cd, meaning cp must equal dp.
From your options, the choice that fits the criteria is:
- cp ~ dp
This indicates that line segment cd is bisected at point p. However, it is also crucial to confirm that ab is indeed perpendicular to cd, which should correspond to another notation (e.g., "ab ⊥ cd").
If we assume "o ab i cd" suggests that ab is perpendicular to cd, then that would confirm both conditions for ab being the perpendicular bisector of cd.
Based solely on the provided options, if forced to choose one, cp ~ dp would be the necessary condition to indicate that ab bisects cd.
If you need more clarification or specific notations to confirm perpendicularity, please provide the available options, or consider that both conditions should be fulfilled for ab to definitively be the perpendicular bisector of cd at point p.