Question

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?

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

Answer 1

An equidistant point is a given point that is at the same distance from two reference points. Thus the appropriate answer is: 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.

An equidistant point is a given point that is at the same distance from two reference points. Thus the point is said to be between the two points and at an equal distance.

A bisector is a line that divides a given line segment or angle into two equal parts or measures.

In the given question, it can be observed that the swings are o be placed in such a way that they would be at the same distance from the jungle gym and monkey bars.

Therefore, the required answer to the question is: 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.

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