Perpendicular Bisector
Is a median, altitude, angle bisector, or perpendicular bisector shown?
The perpendicular bisector of a line segment is a line that intersects the line segment at its midpoint and forms a right angle (90 degrees) with the line segment.
To construct the perpendicular bisector of a line segment, follow these steps:
1. Draw the line segment whose perpendicular bisector you want to find.
2. Use a compass to find the midpoint of the line segment by drawing arcs that intersect each other on opposite sides of the line segment. The point where the arcs intersect is the midpoint.
3. Draw a straight line through the midpoint of the line segment that is perpendicular to the line segment. This line is the perpendicular bisector of the line segment.
The perpendicular bisector has several important properties. One property is that any point on the perpendicular bisector is equidistant to the endpoints of the line segment. This means that if you measure the distance from any point on the perpendicular bisector to each endpoint of the line segment, the distances will be equal.
The perpendicular bisector is also important in determining the circumcenter of a triangle. The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect.
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