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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?

if segment dc bisects segment 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.

if segment dc bisects segment ab, then point d is equidistant from points a and b because congruent parts of congruent triangles are congruent.

if segment ad bisects segment 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.

if segment ad bisects segment ab, then point d is equidistant from points a and b because congruent parts of congruent triangles are congruent.