Question

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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.s the relationship between translations, reflections, and rigid motion?

Answer 1

She can prove the point D. if segment AD ≅ segment CD, then point D is equidistant from points A and B because congruent parts of congruent triangles are congruent

How to illustrate the information?

It should be noted that line CD is a perpendicular line to line ACB intersecting point C. To understand it easier, if ACB is a horizontal lines, D is a point directly on top of C.

In this case, any point directly on C which perpendicular to line ACB will always the same to the endpoint of the segments.

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

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