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?

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

B) 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.

C) If m∠ACD = 90° then point D is equidistant from points A and B because congruent parts of congruent triangles are congruent.

D) 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.

Answer 1

Answer: D if m<ACD = 90 then point D is equally distant from points A and B because a point on a perpendicular bisector is equidistant from the end points of the segment it insects

Explanation:

I took the test and got it right, and AD and CD are not congruent and C just doesn’t make sense sooo

Answer 2

How she can prove that point D is equidistant from the jungle gym and monkey bars

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.

The perpendicular bisector theorem simply states that any point on the perpendicular bisector is simply equidistant from both the endpoints of the line segment on which it is drawn.

Therefore, If a pillar is station at the middle of a bridge at an angle, all the points on the pillar will be equidistant from the end points of the bridge and so, relating to the answer, point D is equidistant from points A and B due to the fact thag a point on a perpendicular bisector is equidistant from the endpoints of the segment it intersects.

Conclusively, Option d is the best option that explains the statement above

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