Select the choice that indicates ⟷/AB is the perpendicular bisector of ⟷/CD if they intersect at P

Question

• AP ≅BP
• AC⊥BD and AP≅BP
• AB ⊥ CD
• CD ⊥ AB and CP≅DP

Answer 1

The correct choice that indicates ⟷/AB is the perpendicular bisector of ⟷/CD if they intersect at point P is:

• CD ⊥ AB and CP≅DP

This is because, for a line segment to be the perpendicular bisector of another segment, it must intersect the segment at its midpoint (which is what CP ≅ DP indicates), and the two segments must be perpendicular at that point of intersection (indicated by CD ⊥ AB).