Question

question 1
beth is planning a playground and has decided to place the swings in such a way that they are the same distance from the jungle gym and the monkey - bars. if beth places the swings at point d, how could she prove that point d is equidistant from the jungle gym and monkey - bars?
a. if ac = bc, then point d is equidistant from points a and b because congruent parts of congruent triangles are congruent.
b. if ac = cd, then point d is equidistant from points a and b because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects.
c. if ac = bc, then point d is equidistant from points a and b because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects.
d. if ad = cd, then point d is equidistant from points a and b because congruent parts of congruent triangles are congruent.

Explanation:

Step1: Recall perpendicular - bisector property

A point on the perpendicular bisector of a line segment is equidistant from the endpoints of the line segment. In the figure, if \(DC\) is the perpendicular bisector of \(AB\) (where \(A\) is the jungle - gym and \(B\) is the monkey - bars), then any point on \(DC\) (such as point \(D\)) is equidistant from \(A\) and \(B\).

Step2: Analyze the options

We need to find the option that correctly states the perpendicular - bisector property.

Answer:

If \(DC\) is the perpendicular bisector of \(AB\), then point \(D\) is equidistant from points \(A\) and \(B\) because a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects.