Select the choice that indicates AB←→

Question

is the perpendicular bisector of CD←→
if they intersect at P
.(1 point)
Responses

AP¯¯¯¯¯¯¯¯≅BP¯¯¯¯¯¯¯¯
Modifying above upper A upper P with bar congruent to Modifying above upper B upper P with bar

CD¯¯¯¯¯¯¯¯⊥AB¯¯¯¯¯¯¯¯
Modifying above upper C upper D with bar perpendicular to Modifying above upper A upper B with bar

AB¯¯¯¯¯¯¯¯⊥CD¯¯¯¯¯¯¯¯
and CP¯¯¯¯¯¯¯¯≅DP¯¯¯¯¯¯¯¯
Modifying above upper A upper B with bar perpendicular to Modifying above upper C upper D with bar and Modifying above upper C upper P with bar congruent to Modifying above upper D upper P with bar

AC¯¯¯¯¯¯¯¯⊥BD¯¯¯¯¯¯¯¯
and AP¯¯¯¯¯¯¯¯≅BP¯¯¯¯¯¯¯¯
Modifying above upper A upper C with bar perpendicular to Modifying above upper B upper D with bar and Modifying above upper A upper P with bar congruent to Modifying above upper B upper P with bar

Answer 1

To determine which choice indicates that line segment \( AB \) is the perpendicular bisector of line segment \( CD \) when they intersect at point \( P \), we look for two conditions:

1. \( AB \) must be perpendicular to \( CD \).
2. \( P \) must be the midpoint of \( CD \), which means \( CP \cong DP \).

The correct choice that indicates \( AB \) is the perpendicular bisector of \( CD \) is:

Choice 3: \( AB \perp CD \) and \( CP \cong DP \)

This states that \( AB \) is perpendicular to \( CD \) and that segments \( CP \) and \( DP \) are congruent, meaning \( P \) is the midpoint of \( CD \).