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To bisect a given angle. |
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To bisect a given angle. |
Given:  ABC |
| Required: To bisect ABC |
| Procedure: |
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Use the compass tool and construct a circle with B as the center. |
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Label the intersection with BA point D, and with BC point E. |
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Use the compass tool and construct a circle with D
as center and a radius greater than 1/2 DE. |
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Label any point on this circle G; use the segment command under the
construct menu and construct a segment congruent to DG, the circle
radius |
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Use the circle by center + radius command under the
construct menu and construct a circle with center E and radius congruent
to segment DG. |
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Label the point of intersection of these two circles F. |
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Use the ray command under the construct menu and construct ray BF. |
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BF bisects ABC. |
| Proof: |
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BD=BE and DF=EF (Radii of = circles are =) |
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BF=BF
(Identity) |
 BDF BEF
(s.s.s.=s.s.s.) |
 DBF=FBE
and ABC
is bisected. (Corresponding parts of ) |
| Sketch: Drag points around on the sketch below. Why does the bisector "disappear" if you drag point A far to the left? Could you modify the construction to control this? |
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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 an angle |
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