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

Answer 1

Beth can prove that point D is equidistant from the jungle gym and monkey bars by showing that triangles ACD and BCD are congruent and that CD is a perpendicular bisector of segment AB.

Step-by-step explanation:

To prove that point D is equidistant from the jungle gym (point A) and the monkey bars (point B), you can use option C: If triangles ACD and BCD are congruent, 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.

In this case, triangle ACD and triangle BCD are congruent because angle ACD measures 90 degrees and angle BCD measures 90 degrees. This means that CD is a perpendicular bisector of segment AB, and any point on the perpendicular bisector is equidistant from the endpoints A and B.