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Topic: Bisector

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perpendicular bisector

angle bisector

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	Bisection - Wikipedia, the free encyclopedia
		The perpendicular bisector of a segment also has the property that each of its points is equidistant from the segment's endpoints.
		The interior bisector of an angle is the line or line segment that divides it into two equal angles on the same side as the angle.
		The exterior bisector of an angle is the line or line segment that divides it into two equal angles on the opposite side as the angle.
	en.wikipedia.org /wiki/Bisector (465 words)

	Geometry Forum Project of the Month - Jan. 1996
		One is that all of the altitudes of the iscoceles triangles are angle bisectors.
		In an isosceles triangle, from the vertex angle, the altitudes are perpendicular bisectors and medians.
		perpendicular bisector: A perpendicular bisector is a line/ray/segment that is perpendicular to a segment at its midpoint.
	mathforum.org /pom/sols2.96.html (7088 words)

	Do Equal Bisectors Imply Isosceles? (Site not responding. Last check: 2007-10-21)
		The bisector of angle A strikes the line BC at point D, and the bisector of angle B strikes the line AC at point E. Notice that if we set a = 60 degrees and b = 165.867 degrees the two bisectors are both of length 0.9003 units, and yet the triangle is NOT isosceles.
		In general, the angle bisectors strike the opposite sides at the points [Lcos(a),Lsin(a)] and [1-Lcos(b),Lsin(b)] where L is the length of the bisectors.
		We know the "bisector" must pass through point B, and the angles between the bisector and the lines AB and BC must be equal, but these conditions are satisfied by both of the principal bisectors.
	www.mathpages.com /home/kmath433.htm (592 words)

	Triangle -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-21)
		A (additional info and facts about perpendicular bisector) perpendicular bisector of a triangle is a straight line passing through the midpoint of a side and being perpendicular to it, i.e.
		An (additional info and facts about angle bisector) angle bisector of a triangle is a straight line through a vertex which cuts the corresponding angle in half.
		The three angle bisectors intersect in a single point, the center of the triangle's (additional info and facts about incircle) incircle.
	www.absoluteastronomy.com /encyclopedia/t/tr/triangle.htm (2236 words)

	Bisection (Site not responding. Last check: 2007-10-21)
		In diatonic set theory a bisector divides the octave approximately in half and may be used in place of a generator to derive collections for which structure implies multiplicity is not true such as the ascending melodic minor, harmonic minor, and octatonic scales.
		Rahn also uses aliquant bisector for bisectors which may be used to generate every note in a collection, in which case the bisector and the number of notes must be coprime.
		Bisectors may be used to produce the diatonic, harmonic minor, and ascending melodic minor collections.
	www.worldhistory.com /wiki/B/Bisection.htm (597 words)

	Bisector (Site not responding. Last check: 2007-10-21)
		We construct the bisector by connecting the midpoints of horizontal line segments spanning the width of the profile at a number of depths.
		The amount of curvature, or equivalently the span of velocity covered by the bisector is a measure of the strength of the granulation on the star's surface.
		Variations in a star's line bisectors are known to arise from 1) changes in the convection during decade-long magnetic cycles, 2) Doppler shifts arising from oscillations on the star's surface, 3) surface features on the star carried across the face of the star as the star rotates.
	www.astro.uwo.ca /~dfgray/bisector.html (319 words)

	PlanetMath: angle bisector
		For every angle, there exists a line that divides the angle into two equal parts.
		For a triangle, the point where the angle bisectors of the three angles meet is called the incenter.
		This is version 1 of angle bisector, born on 2002-11-27.
	planetmath.org /encyclopedia/ExteriorAngleBisector.html (113 words)

	Human Factors at NASA Ames Research Center - Publications (Site not responding. Last check: 2007-10-21)
		In experiment 2, subjects' errors while reaching to the imaginary bisector of the Judd illusion were consistent with the presence of an illusion of bisector location.
		However, when a bisector line was added to the Judd figure, reaching errors were similar to those obtained with a control figure.
		The results of the experiments indicate that hand-eye coordination is biased in the direction of illusions of bisector location only when no target is present at the intended goal of the reaching response and subjects are required instead to form a mental image of the target.
	human-factors.arc.nasa.gov /web/library/publications/publications_details.php?id=34 (441 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		On Rational Bisector and Alpha-Sectors* Gershon Elber Department of Computer Science Technion, Israel Institute of Technology Haifa 32000, Israel Given two varieties in Rn, their bisector is defined as the set of points which are equidistant from the two varieties.
		The bisector surface in R3 of several CSG primitives such as a cone and a sphere, or a plane and a cone.
		The alpha-sector extends the notion of the bisector to arbitrary distance ratios between the two varieties.
	www.cs.utah.edu /dept/colloq/1999-00/gershon.html (228 words)

	The Bisector Surface of Rational Space Curves - Elber, Kim (ResearchIndex)
		However, in general, the bisector of two rational curves in the plane is not rational [3].
		Moreover, given two rational space curves, we show that the bisector surface is rational (except for the degenerate case in which the two curves are coplanar).
		showed that the bisector surface of two rational space curves in IR 3 is indeed a rational surface, except for the degenerate case in...
	citeseer.ist.psu.edu /elber98bisector.html (459 words)

	Practice Quiz 1 (Site not responding. Last check: 2007-10-21)
		Which is not a property of the Perpendicular Bisector of a triangle?
		any point on the perpendicular bisector is equidistant from each of the sides of a triangle.
		any point on the perpendicular bisector is equidistant from the vertices of the triangle.
	www.cat.cc.md.us /~kcomp/chap_one_quiz_two.htm (109 words)

	Ratio:Sides of a Triangle to Segments cut by an Angle Bisector (Site not responding. Last check: 2007-10-21)
		Construct an angle bisector in the triangle and draw the segment along the angle bisector from the vertex to the intersection with the opposite side.
		The bisector of an angle of a triangle divides the opposite side into segments that are proportional to the adjacent sides.
		Prove that the bisector of an exterior angle of a triangle divides the opposite side externally into segments that are proportional to the adjacent sides.
	jwilson.coe.uga.edu /emt725/Bisect/bisect.html (223 words)

	Incenter Investigation (Site not responding. Last check: 2007-10-21)
		In this section of the exploration you will be asked to discover the way the angle bisectors of a triangle relate to each other and to the sides of the triangle.
		The angle bisector of an angle ABC is the ray BE in the interior of angle ABC such that the measure of angle ABE is equal to the measure of angle CBE.
		Remember that we are studying the lengths of the perpendicular segments from M to the sides and that M lies on the angle bisectors.
	www.geom.uiuc.edu /~demo5337/Group2/incenter.html (548 words)

	SparkNotes: Constructions: Dividing Angles and Segments
		With angle bisectors and trisectors, it also holds true that any of the new angles created by the bisector or trisector is equal to exactly one-half or one-third of the original angle, depending on whether the angle has been bisected or trisected.
		There are an infinite number of bisectors for every segment, depending on the angle at which the incoming segment or line bisects the other segment.
		If a bisector is perpendicular to the segment it bisects, it is called the perpendicular bisector of that segment.
	www.sparknotes.com /math/geometry1/constructions/section5.rhtml (445 words)

	1377
		The Bisector is a part, which has a yoke configuration at the top and a 360º ridged skirt at the bottom.
		The rigid skirt at the bottom is located between a pair of hub spring units, which encircle the outer side and the inner side of this skirt.
		It has previously been mentioned that the Bisector skirt is located between the outer and the inner ring of hub springs.
	www.synchrolite.com /1377.html (1862 words)

	Formal Constructions: Part 1
		Bisector of a line segment: constructing a bisector of a line segment.
		This procedure is also used to construct a perpendicular bisector.
		Angles: constructing an angle congruent to a given angle and constructing an angle bisector.
	www.teacherlink.org /content/math/interactive/geoweb/lessons/construction1/home.html (229 words)

	Homework 6 Solutions (Site not responding. Last check: 2007-10-21)
		Perpendicular bisector: The perpendicular bisector of a line segment AB is the set of all points which are equidistant from A and B. Proof by Laura Evans, Laura Fillingim, Erin Cain, and Melissa Chaffin:
		The angle bisector of Angle P intersects line segment AB at Point D. Using the Congruence axiom SAS, we know that Triangle APD is congruent to Triangle BPD.
		Therefore, because DP bisects and is perpendicular to AB, PD is the perpendicular bisector of AB.
	www.math.uga.edu /~clint/2004/5200/hw6sol.htm (3673 words)

	Perpendicular Bisector - interactive applet
		The definition and properties of the perpendicular bisector are explored using a geometry applet.
		The perpendicular bisector of a line segment AB is a line that is perpendicular to AB and passes through the midpoint of segment AB.(see figure below).
		A large screen applet is used to explore the definition and properties of the perpendicular bisector.
	www.analyzemath.com /Geometry/PerpendicularBisector/PerpendicularBisector.html (296 words)

	Chapter Two (Site not responding. Last check: 2007-10-21)
		If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
		If a point is on the bisector of an angle, then the point is equidistant from the sides of the angle.
		If a point in the interior of an angle is equidistant from the sides of the angle, then the point is on the angle bisector.
	pages.cthome.net /jfleary/2gnf4/2gn4c5/2gn4(5-2).htm (133 words)

	Perpendicular Bisectors (Site not responding. Last check: 2007-10-21)
		The perpendicular bisector theorem states that if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
		In this illustration, segment AB is bisected by line CD intersecting it at its midpoint E. According to the theorem, point F, which is on the perpendicular bisector, should be equidistant to points A and B at all times.
		The perpendicular bisector converse theorem, on the other hand, states that if a point is equidistant from the endpoints of a segment, then the point lies on the perpendicular bisector of the segment.
	marian.creighton.edu /~dkath/PerpendicularBisector.htm (193 words)

	e-z Java Applets 1-6 Angle Bisector (Site not responding. Last check: 2007-10-21)
		We also learn that by definition the angle bisector divides an angle into two congruent angles.
		What we don't learn is an important property about all points on the angle bisector.
		Move point D up and down the angle bisector and adjust the angle size.
	www.e-zgeometry.com /java/1.6anglebisector.asp (98 words)

	CSUSB Math 129: Constructing perpendiculars
		Definition: The perpendicular bisector of a segment is the line that is perpendicular (at a right angle) to the segment and goes through the midpoint of the segment.
		Theorem: The perpendicular bisector of a segment is the set of all points that are the same distance from both the endpoints of the segment.
		The main idea is to construct an appropriate line segment on the line, then construct the perpendicular bisector of this segment.
	www.math.csusb.edu /courses/m129/perp.html (801 words)

	Construction: Bisect Angle (Site not responding. Last check: 2007-10-21)
		Definition The bisector of an angle is a ray whose end point is the vertex of the angle and which divides the angle into two equal angles.
		Draw an arc that is centered at the vertex of the angle.
		Since the intersection points and the vertex all lie on the angle bisector, we know that the line which passes through these points must be the angle bisector.
	www.coe.tamu.edu /~strader/geometry/bisectangle1.0/bisectangle.html (579 words)

	Triangles, Bisectors and Circumcircles - interactive applet
		The properties of perpendicular bisectors in triangles and circumcircles are explored interactively using a geometry java applet.
		Let L1 be the perpendicular bisector (line through the midpoint of the opposite side to vertex A and perpendicular to this side) of segment BC, L2 the perpendicular bisector of AC and L3 the perpendicular bisector of AB.
		The point of intersection of the bisectors (circumcenter) is on one side of the triangle.
	www.analyzemath.com /Geometry/Circumcircle/Circumcircle.html (337 words)

	MATH 302: Topics in Geometry
		Task: Try to construct the perpendicular bisector of the line segment, j (the line between the two points in the construction from section 2), with a ruler and compass.
		Proposition: For an isoceles triangle, the bisector of the angle formed by the two edges of equal length is the perpendicular bisector of the remaining edge.
		In this section, we'll construct the bisector of an angle using a ruler and compass (same rules apply as in section 4).
	www.math.uiuc.edu /~stolman/m302/labs/labs/lab2.html (1715 words)

	mesh
		Geometry Bisector: After the boundary conditions are implemented, the user is asked to pick the geometry bisector, with the help of a dialog box.
		The valid combinations of selection of geometry bisector are vertex-vertex, vertex-edge, edge-vertex and edge-edge.
		The geometry bisector, if a good selection is made, results in a good flow in the final block topology of the given geometry.
	www.eng.uc.edu /icams/research/mesh/mesh.htm (2182 words)

	Untitled Document (Site not responding. Last check: 2007-10-21)
		An angle bisector is constructed at vertex C and meets the opposite side at point D. We will refer to segment BC as a, segment CA as b, segment BD as x, and segment DA as y.
		Notice that the ratio of the adjacent sides of the triangle and the ratio of the segments cut off by the bisector are the same.
		Next we will go on to prove that the bisector of an exterior angle of a triangle divides the opposite side externally into segments that are proportional to the adjacent sides.
	jwilson.coe.uga.edu /EMT668/EMAT6680.F99/Tarleton/6990-Explo_3/exploration_3.html (222 words)

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