Question

Select the choice that indicates AB is the perpendicular bisector of CD if they intersect at P.
A:-- CD I AB
B:AB I CD and CP~=

Answer 1

To determine the correct condition that indicates AB is the perpendicular bisector of CD, we need to establish two criteria:

1. The lines AB and CD must intersect at point P.
2. The intersection must occur at a right angle (90 degrees), and point P must be the midpoint of segment CD, meaning that CP is equal to PD.

Based on the provided choices:

A: CD I AB (This states that CD is perpendicular to AB but doesn't indicate that P is the midpoint of CD.)
B: AB I CD and CP ~= PD (This states that AB is perpendicular to CD and that CP is equal to PD, indicating that P is the midpoint of CD.)

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

**B: AB I CD and CP ~= PD**