perpendicular bisector
cuts a side perfectly in half AND intersects at a 90° angle
A perpendicular bisector is a line, segment, or ray that is perpendicular to a given line segment and divides it into two equal parts. In other words, it is a line that intersects a line segment at its midpoint and forms a right angle with it.
To construct a perpendicular bisector for a given line segment, we first find the midpoint of the line segment by taking the average of its x-coordinates and y-coordinates. Then, we draw a line that passes through the midpoint and is perpendicular to the given line segment.
The perpendicular bisector has several important properties, including:
– It is equidistant from the endpoints of the line segment.
– If two points lie on the perpendicular bisector, then they are equidistant from the endpoints of the line segment.
– In a triangle, the perpendicular bisectors of the sides intersect at a point called the circumcenter, which is the center of the circumcircle that passes through all three vertices.
The concept of perpendicular bisectors is important in geometry and other fields, as it provides a way to divide objects into equal parts and to find important geometric centers and properties of shapes.
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