2. If a point is equidistant from the endpoints of a segment then it must be the midpoint of the segment
3. The set of all the points in the plane that are a given distance from a line segment is a pair of lines parallel to the given segment.HELP GEOMETRY identify these statements as either true or false. If false please explain why it is false?
1. False, but almost true. A trapezoid is a quadrilateral with *at least* one pair of parallel sides. Parallelograms are also trapezoids. If we were to discount parallelograms from being trapezoids, then it would be true.
2. False. If the point were guaranteed to be on the segment, then it would be true. Currently, the most we can say is that the point lies on the perpendicular bisector of the segment.
3. False. If the segment were a line, then this would be true, but because this is a segment which terminates at an endpoint somewhere, the set of all points of fixed distance will form a semicircle around the point.
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