Would My Answer be correct?

Question

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  ≅ , then point D is equidistant from points A and B because congruent parts of congruent triangles are congruent. 

If  ≅ , 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  ≅ , 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  ≅ , then point D is equidistant from points A and B because congruent parts of congruent triangles are congruent.

I think it would be option 3 but I am not sure, is it correct if not give me the correct answer please.

Answer 1

Yes, you are correct. Option 3 is based on the fact that segment AC and BC are congruent which makes point C a midpoint. The sketch gives segment AB perpendicular to BC. These mean that BC IS a perpendicular bisector.

You could also argue that option 1 is correct but there are some steps missing that lead to their conclusion.