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angle bisector as locus
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(Definition)
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If $0 < \alpha < 180^{\mathrm{o}}$ , then the angle bisector of $\alpha$ is the locus of all such points which are equidistant from both sides of the angle. (It is proved by using the AAS and SSA theorems.)
The equation of the angle bisectors of all four angles formed by two intersecting lines
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(1) |
is
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which may be written in the form
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(3) |
after performing the divisions in (2) termwise; the angles $\alpha_1$ and $\alpha_2$ mean then the slope angles of the lines.
Note. The two lines in (2) are perpendicular, since their slopes $\displaystyle\frac{\sin\alpha_1\pm\sin\alpha_2}{\cos\alpha_1\pm\cos\alpha_2}$ are opposite inverses of each other.
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"angle bisector as locus" is owned by pahio.
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Cross-references: opposite inverses, slopes, perpendicular, slope angles, divisions, lines, equation, theorems, SSA, AAS, angle, sides, points, locus, angle bisector
There is 1 reference to this entry.
This is version 7 of angle bisector as locus, born on 2007-06-01, modified 2009-02-10.
Object id is 9492, canonical name is AngleBisectorAsLocus.
Accessed 2354 times total.
Classification:
| AMS MSC: | 51N20 (Geometry :: Analytic and descriptive geometry :: Euclidean analytic geometry) |
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Pending Errata and Addenda
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