Question

Constructing Parallel and Perpendicular Lines Quick Check 2 of 52 of 5 Items Question Select the choice that indicates AB←→ is the perpendicular bisector of CD←→ if they intersect at P .(1 point) Responses CD¯¯¯¯¯¯¯¯⊥AB¯¯¯¯¯¯¯¯ Modifying above upper C upper D with bar perpendicular to Modifying above upper A upper B with bar AP¯¯¯¯¯¯¯¯≅BP¯¯¯¯¯¯¯¯ Modifying above upper A upper P with bar congruent to Modifying above upper B 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 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 Skip to navigation page 14 of 15 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

Answer 1

To indicate that line segment \( \overleftrightarrow{AB} \) is the perpendicular bisector of segment \( \overleftrightarrow{CD} \) when they intersect at point \( P \), we need to mention two critical characteristics:

1. **Perpendicularity**: The two lines intersect at right angles.
2. **Bisection**: The point of intersection divides the segment \( \overline{CD} \) into two equal parts.

Considering the options you provided, the correct choice would be:

**\( \overline{AB} \perp \overline{CD} \) and \( CP \cong DP \)**.

This indicates that \( AB \) is perpendicular to \( CD \) and that the segments \( CP \) and \( DP \) are congruent, satisfying the conditions of being a perpendicular bisector.