Select the choice that indicates AB←→ 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
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
CD¯¯¯¯¯¯¯¯⊥AB¯¯¯¯¯¯¯¯
Modifying above upper C upper D with bar perpendicular to Modifying above upper A upper B 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
explain
The correct choice is:
CD¯¯¯¯¯¯¯¯⊥AB¯¯¯¯¯¯¯¯
This option indicates that AB←→ is perpendicular to CD←→. The symbol "⊥" is used to represent perpendicularity.
The other choices do not indicate that AB←→ is the perpendicular bisector of CD←→. They either refer to the congruence of segments AP←→ and BP←→ (which is not relevant to determining the perpendicular bisector) or the congruence of segments CP←→ and DP←→ (which is also not relevant to determining the perpendicular bisector).
The correct choice that indicates AB←→ is the perpendicular bisector of CD←→ if they intersect at P is:
AB¯¯¯¯¯¯¯¯⊥CD¯¯¯¯¯¯¯¯ and CP¯¯¯¯¯¯¯¯≅DP¯¯¯¯¯¯¯¯
To determine if AB←→ is the perpendicular bisector of CD←→ at point P, we need to consider two conditions:
1) AB←→ is perpendicular to CD←→
2) CP¯¯¯¯¯¯¯¯ is congruent to DP¯¯¯¯¯¯¯¯
Looking at the given options, the correct choice is:
AB¯¯¯¯¯¯¯¯⊥CD¯¯¯¯¯¯¯¯ and CP¯¯¯¯¯¯¯¯≅DP¯¯¯¯¯¯¯¯
Explanation:
- The first part of the choice, AB¯¯¯¯¯¯¯¯⊥CD¯¯¯¯¯¯¯¯, states that AB←→ is perpendicular to CD←→. This means that the two lines intersect at a right angle.
- The second part of the choice, CP¯¯¯¯¯¯¯¯≅DP¯¯¯¯¯¯¯¯, states that CP¯¯¯¯¯¯¯¯ is congruent to DP¯¯¯¯¯¯¯¯. This means that the distances from P to C and P to D are the same.
By satisfying both conditions, AB←→ is the perpendicular bisector of CD←→ at point P.