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(02.03 mc)

triangle adb, point c lies on segment ab and forms segment cd, segment ac is congruent to segment bc. point a is labeled jungle gym and point b is labeled monkey bars.

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 ad ≅ segment cd, then point d is equidistant from points a and b because congruent parts of congruent triangles are congruent.
if segment ad ≅ segment 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.
if m∠acd = 90° then point d is equidistant from points a and b because congruent parts of congruent triangles are congruent.
if m∠acd = 90° 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.