To construct the perpendicular bisector of line segment using a compass and ruler, follow these steps:
Draw on paper.
Set the compass to a width greater than half of .
Draw arcs above and below from points and .
Mark the intersection points and where the arcs cross.
Draw the line connecting and . This line is the perpendicular bisector of .
This bisector is perpendicular to and divides it into two equal parts.
Solution
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To construct the perpendicular bisector of line segment , start by placing the compass point on point and drawing an arc above and below the line segment. Without changing the width, repeat this process with the compass point on point . The two arcs will intersect at two points above and below the line segment. Connect these two intersection points with a straightedge, and voilà! You’ve created the perpendicular bisector, which will intersect at its midpoint at a right angle.
Fun fact: The perpendicular bisector has some cool properties! Any point on this line is equidistant from points and . This theorem is often used in navigation and engineering to determine locations equidistant from two points, making it quite handy in real life!