Select the choice that indicates AB←→

Question

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

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

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

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

CD¯¯¯¯¯¯¯¯⊥AB¯¯¯¯¯¯¯¯

Answer 1

When a line segment \( AB \) is the perpendicular bisector of another segment \( CD \), it means that:

1. \( AB \) is perpendicular to \( CD \) (\( AB \perp CD \)).
2. The point of intersection \( P \) divides \( CD \) into two equal segments, meaning \( CP \cong DP \).

Given your choices, the correct statements that characterize \( AB \) as the perpendicular bisector of \( CD \) are:

• \( AB \perp CD \)
• \( CP \cong DP \)

Thus, the correct choice would be:

AB¯¯¯¯¯¯¯¯⊥CD¯¯¯¯¯¯¯¯ and CP¯¯¯¯¯¯¯¯≅DP¯¯¯¯¯¯¯¯