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angle bisector as locus∗ pahio† 2013-03-21 23:04:16 If 0 < α < 180o , then the angle bisector of α 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 a1 x+b1 y+c1 = 0, a2 x+b2 y+c2 = 0 (1) is a2 x+b2 y+c2 a1 x+b1 y+c1 p = ± p 2 2 , 2 2 a1 +b1 a2 +b2 (2) which may be written in the form x sin α1 − y cos α1 + h1 = ±(x sin α2 − y cos α2 + h2 ) (3) after performing the divisions in (2) termwise; the angles α1 and α2 mean then the slope angles of the lines. sin α1 ± sin α2 Note. The two lines in (2) are perpendicular, since their slopes cos α1 ± cos α2 are opposite inverses of each other. ∗ hAngleBisectorAsLocusi created: h2013-03-21i by: hpahioi version: h39492i Privacy setting: h1i hDefinitioni h51N20i † This text is available under the Creative Commons Attribution/Share-Alike License 3.0. You can reuse this document or portions thereof only if you do so under terms that are compatible with the CC-BY-SA license. 1