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To bisect a given line segment. |
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To bisect a given line segment. |
| Given: Line segment AB |
| Required: To bisect AB |
| Procedure: |
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With A as a center and with a radius greater than 1/2 AB, use the
compass tool to construct a circle. |
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Label any point on this circle G. |
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Use the segment command under the construct menu to construct a segment congruent to
AG, the circle radius. |
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Use the circle by center + radius command under the
construct menu to construct a circle with B as a center and radius
congruent to segment AG. |
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Label the intersections of these two circles as C and D. |
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Use the segment command under the construct menu
and construct segment CD intersecting AB at point
E. |
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AB is bisected at E. |
| Proof: |
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Since radii of equal circles are equal, C and D are equidistant from A
and B. |
CD is the 
bisector
of AB at E. ( Two points each equidistant from the extremities of
a line segment determine the
bisector of that line segment.) |
| Sketch: On the sketch below drag point A around; do you always have a bisector? Does it matter whether A is to the right or left of B? |
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This page uses JavaSketchpad, a World-Wide-Web component of The Geometer's Sketchpad. Copyright © 1990-2001 by KCP Technologies, Inc. Licensed only for non-commercial use. bisect a line segment |
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