How to Learn Perpendicular Bisectors in Math
Perpendicular bisectors are perpendicular lines that pass through the midpoint of a line segment. While you can draw a perpendicular bisector simply by using a ruler to determine the midpoint of a line segment, the point equidistant from both ends of the line segment, and drawing a line at ninety degrees to the line segment at that point, learning about perpendicular bisectors in a larger geometrical context is a more effective way of assimilating the usefulness of a perpendicular bisector.
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Instructions
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Use a ruler to draw a line segment. Label the endpoints "A" and"'B."
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Set the compass width to approximately 2/3 of the length of the line segment, although the actual width of the compass does not matter. Place the point of the compass on point "A," and draw an arc above your line segment. Leaving your compass on point "A," draw an arc beneath your line segment. Move the point of your compass to point "B," keeping the width of the compass the same. Draw an arc above and below your line segment. Notice that your arcs above your line segment intersect, and your arcs beneath your line segment intersect.
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Use a pencil to make two marks at the points of intersection of your arcs, above and beneath your line segment. Label the mark above "C," and label the mark below "D." Use a ruler to connect the two marks. You have constructed your perpendicular bisector.
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Use a ruler to connect point "C" to points "A" and "B." Likewise, use a ruler to connect point "D" to points "A" and "B." Notice that you have constructed two isosceles triangles, one on top of the other. Sides AC, BC, AD, and BD are all of equal length. Likewise, angles CAB, CBA, DAB, and DBA are all equal in magnitude to each other, and angle ACB is equal in magnitude to angle ADB. This information can be important when you need to use geometry or trigonometry to quantify the angles or lengths of a figure with perpendicular bisectors.
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