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select the choice that indicates AB is the perpendicular bisector of CD if they intersect at P.

a. AP~BP
b. AB CD and CP~DP
c. AC BD and AP~BP
d. CD AB

1 answer

To indicate that line segment AB is the perpendicular bisector of segment CD, we need that:

  1. AP is equal to BP (which means A and B are equidistant from point P where they intersect).
  2. AB is perpendicular to CD (which means it intersects CD at a right angle).

From your choices, the correct option that indicates AB is the perpendicular bisector of CD is:

a. AP ~ BP

However, none of the options directly state that AB is perpendicular to CD. Therefore, the best answer from the listed choices would be a, as it implies the equidistance required. Note that for the complete definition, it would be ideal to also have the perpendicularity condition.