Question

When constructing a perpendicular bisector of a segment, why should you make arcs with the same radius from each endpoint? Select the true statement.

a. this makes the arcs perpendicular to each other
b. this makes the arcs equidistant from each other
c. this makes the intersections of the arcs equidistant from the endpoints
d. this makes the arcs parallel to the segment

Answer 1

Answer: it’s c

Explanation:

I’m smart

Answer 2

c. this makes the intersections of the arcs equidistant from the endpoints

Explanation:

You want to know why you should make intersecting arcs using the same radius from the endpoints of a segment to construct its perpendicular bisector.

Perpendicular bisector

Every point on a perpendicular bisector of a segment is equidistant from the end points of the segment. Arcs drawn from the endpoints using the same radius will define a locus of points that are that distance from the endpoint. Where the arcs intersect, the point of intersection is the same distance from both endpoints, hence on the perpendicular bisector.

The described construction ...

makes the intersections of the arcs equidistant from the endpoints, choice C

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