Construction 5: To bisect a given line segment (to construct the perpendicular bisector of a given line segment) Given:

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Construction 5 To Bisect A Given Line Segment To Construct The Perpendicular Bisector Of A Given Line Segment Given 1 (138.39 KiB) Viewed 51 times

Construction 5: To bisect a given line segment (to construct the perpendicular bisector of a given line segment) Given: Line segment AB To construct: The perpendicular bisector of AB Construction: With A as center and a radius of more than half of AB, construct arc (1). With B as center and the same radius, construct arc (2) intersecting arc (1) at C and D. Draw CD. CD is the required perpendicular bisector of AB. (Two points each equidistant form the ends of a segment determine the perpendicular bisector of the segment.) Explanation: CD is the 1 bisector of AB since points equidistant from the ends of a line segment determine the 1 bisector of the segment. Also the intersection of CD and AB is the midpoint of AB by definition of midpoint (AM = MB)