triangle adb, point c lies on segment ab and forms segment cd, angle acd measures 90 degrees. 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?

1. if segment ac ≅ segment bc, then point d is equidistant from points a and b because congruent parts of congruent triangles are congruent.

2. 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.

3. if segment ac ≅ segment 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.

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