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Topic: Vertical angles

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	Measuring Vertical Angles
		The vertical circle and the vertical vernier of
		A vertical angle is the angle measured vertically
		inclination of the vertical axis and the collimation
	www.tpub.com /engbas/13-11.htm (302 words)

	Building Blocks - Angles and intersecting lines - In Depth (Site not responding. Last check: 2007-10-25)
		In this diagram, angles a and c are vertical angles, and angles b and d are vertical angles.
		The angles that lie in the interior area, or the area between the two lines that are cut by the transversal, are called interior angles.
		Angles a and h, and b and g, are alternate exterior angles.
	www.math.com /school/subject3/lessons/S3U1L5DP.html (273 words)

	Angles (Site not responding. Last check: 2007-10-25)
		Alternate Interior Angles- For any pair of parallel lines 1 and 2, that are both intersected by a third line, such as line 3 in the diagram below, angle A and angle D are called alternate interior angles.
		Alternate Exterior Angles- For any pair of parallel lines 1 and 2, that are both intersected by a third line, such as line 3 in the diagram below, angle A and angle D are called alternate exterior angles.
		Corresponding Angles- For any pair of parallel lines 1 and 2, that are both intersected by a third line, such as line 3 in the diagram below, angle A and angle C are called corresponding angles.
	www.mec.edu /gltech/library/April_geometry/angles.html (326 words)

	Pairs Of Angles
		Some examples are complementary angles, supplementary angles, vertical angles, alternate interior angles, alternate exterior angles and corresponding angles.
		Two angles are called complementary angles if the sum of their degree measurements equals 90 degrees.
		One way to remember alternate exterior angles is that they are the vertical angles of the alternate interior angles.
	www.onlinemathlearning.com /pairs-of-angles.html (579 words)

	Surveying instrument - Patent 3934353
		The plate is suspended from a point on the vertical axis through the center of gravity of said plate, and a hairline extends across said plate and mirrored reflection surface in a direction perpendicular to the vertical suspension axis.
		Vertical angles in degrees are measured on line 27 when the instrument is positioned at a predetermined distance from the user's eye, by holding the free end of cord 32 against the user's forehead while simultaneously holding the instrument away from the user so that the cord is tight (FIG.
		Angles greater than those which can be read on line 27 and 28 are measured when predetermined distance cord 32 length B is used to position the instrument at the corresponding distance from the user's eye, while reading degrees on line 30 and percentage of slope on line 31.
	www.freepatentsonline.com /3934353.html (2285 words)

	Angles and Lines
		Angles separate their plane into three regions: the angle; the region inside or interior to the angle; and the region outside or exterior to the angle.
		The angle between two sides of a polygon is an interior angle, whereas the angle formed by one side and extending the other side of an angle in a polygon is an exterior angle.
		Angles inside circles are either central angles if their vertex is the center of the circle, or inscribed angles if their vertex is on the circle.
	www.andrews.edu /~calkins/math/webtexts/geom03.htm (2908 words)

	Complementary, Supplementary, and Vertical Angles
		Vertical angles are two angles whose sides form two pairs of opposite rays.
		In the triangle shown below, the angles A and B are complementary because they have a sum of 90º.
		This is obvious since angle C is 90º and the other two angles must have a sum of 90º so that the three angles in the triangle together have a sum of 180º.
	www.algebralab.org /lessons/lesson.aspx?file=Geometry_AnglesComplementarySupplementaryVertical.xml (411 words)

	SparkNotes: Constructions: Angle Pairs
		A pair of angles whose sum is 90 degrees are called complementary angles.
		A single angle, when considered alone, can be neither supplementary nor complementary--it can only take on one of these properties when considered as one of a pair of angles.
		These angles, which are formed by rays that point in opposite directions, are called vertical angles.
	www.sparknotes.com /math/geometry1/constructions/section2.rhtml (198 words)

	Angles and angle terms
		An acute angle is an angle measuring between 0 and 90 degrees.
		An obtuse angle is an angle measuring between 90 and 180 degrees.
		An angle bisector is a ray that divides an angle into two equal angles.
	www.mathleague.com /help/geometry/angles.htm#whatisanangle (516 words)

	CVO Website - Chadwick, et.al., 1985, Measurements of slope distances and vertical angles at Mount Baker and Mount ...
		Measurements of slope distances and vertical angles at Mount Baker and Mount Rainier, Washington, Mount Hood and Crater Lake, Oregon, and Mount Shasta and Lassen Peak, California, 1980-1984
		Slope distances were measured with an EDM (Hewlett-Packard 3808A) and vertical angles with a theodolite (Wild T-2, both old and new styles) from benchmarks generally at low elevations around each volcano to reflectors at benchmarks high on the cones.
		Vertical angles were measured primarily to establish station elevations and to make mark-to-mark distance reductions; they were not measured reciprocally (table 2).
	vulcan.wr.usgs.gov /Volcanoes/Cascades/Publications/OFR85-205/OFR85-205.html (3736 words)

	All Elementary Mathematics - Study Guide - Geometry - Angles...
		Angle is a geometric figure (Fig.1), formed by two rays OA and OB (sides of an angle), going out of the same point O (a vertex of an angle).
		A measure of an angle is a value of a turn around a vertex O, that transfers a ray OA to the position OB.
		An angle of 90 deg (Fig.2) is called a right or direct angle; an angle lesser than 90 deg (Fig.3), is called an acute angle; an angle greater than 90 deg (Fig.4), is called an obtuse angle.
	www.bymath.com /studyguide/geo/sec/geo3.htm (406 words)

	Field Techniques (Site not responding. Last check: 2007-10-25)
		For example, if a field worker needed to calculate the height of a tree or a cliff, or the depth of a canyon (a vertical distance), she or he could do so without having to climb the object or feature, thereby risking life and limb.
		The difference between these two vertical angles is the height (or depth) of the object.
		Hold the compass in a vertical plane, with the sighting arm pointed toward your eye, but approximately one foot away so that the point being sighted and the axial line in the sighting window can be focused clearly.
	uts.cc.utexas.edu /~wd/courses/373F/notes/lec12ver.html (631 words)

	angles (Site not responding. Last check: 2007-10-25)
		Vertical angles are 2 angles connected together at their vertex, with both of the angles sharing the two lines making them.
		Among these are obtuse angles, corresponding angles, and vertical angles.
		Two angles are vertical if their side forms 2 pairs of opposite rays.
	www.cobb.k12.ga.us /~smitha/ANGLES.html (394 words)

	SparkNotes: SAT Math Level 2: Lines and Angles
		In this figure, angles 1 and 4 are vertical angles (and therefore congruent), as are angles 2 and 3.
		Alternate exterior angles are pairs of congruent angles on opposite sides of the transversal, outside of the space between the parallel lines.
		Alternate interior angles are pairs of congruent angles on opposite sides of the transversal in the region between the parallel lines.
	www.sparknotes.com /testprep/books/sat2/math2c/chapter6section1.rhtml (787 words)

	Parallel Lines Discussion (Site not responding. Last check: 2007-10-25)
		Supplementary angles are angles that add up to 180 degrees, so that if you put them all together they would form a straight line at the bottom.
		Vertical angles are angles that are formed by the same two lines so one angle is one side of the intersection and the other angle is the other side.
		Corresponding angles are angles that are in the same place relative to the nearest parallel line.
	www.shodor.org /interactivate/discussions/parallelines.html (1592 words)

	ch1
		Angles are formed as a result of intersecting lines.
		Two angles whose sides are opposite rays of each other are called vertical angles.
		This means that <1 and <3 are vertical angles and have the same measure.
	www.csun.edu /~ayk38384/notes/mod5/ch1.htm (429 words)

	Section2
		An angle is a geometric figure that consists of two rays that share a common endpoint.
		The constructed angle will be unique in a sense that if we construct one more angle with the same degree measure and in the same half-plane then this second angle will coincide with the first one.
		Given: a pair of vertical angles AOB and COD and a pair of vertical angles BOD and AOC.
	www.math.psu.edu /geom/koltsova/section2.html (570 words)

	ClickATutor Tutorials
		The measures of a pair of vertical angles are always equal.
		Each of these angles is supplementary to the angle formed by the transversal and the straight line it intersects, but on the opposite side of the transversal.
		The sum of the measures of two adjacent angles formed by such intersection of two straight lines is 180º.
	www.clickatutor.com /BasePUB.asp?pid=2343 (156 words)

	Vertical Angles (Site not responding. Last check: 2007-10-25)
		When two lines cross, 4 angles are formed.
		These are called vertical angles, on opposite sides of p.
		By the same reasoning, w and y are vertical angles, and are congruent.
	www.mathreference.com /geo,vert.html (134 words)

	geo1-6notes (Site not responding. Last check: 2007-10-25)
		Two angles are vertical angles if their sides form two pairs of opposite rays.
		Two angles are complementary angles if the sum of their measures is 90 degrees.
		Example: The measure of the supplement of an angle is four times the measure of the complement of the same angle.
	www2.ops.org /NORTH/curriculum/math/holley/geohtml04/geo1-6notes.html (181 words)

	Types of Triangles
		The definitions above apply to angles when we look at one angle alone, but there are also some special relationships between pairs of angles.
		Complementary angles can be placed so that they form perpendicular lines.
		Supplementary angles can be placed so that they form a straight line.
	regentsprep.org /Regents/math/angles/LAngles.htm (125 words)

	Geometry Session 4, Part B: Parallel Lines
		When two lines intersect, the vertical angles (angles opposite each other) have the same measure.
		When two parallel lines both intersect a third line, corresponding angles (angles in the same relative positions, like angles 1 and 7 or angles 3 and 5 in the picture below) have the same measure.
		You may want to use the facts about corresponding angles and vertical angles, or you may come up with another explanation.
	www.learner.org /channel/courses/learningmath/geometry/session4/part_b/reasoning.html (338 words)

	Vertical Angles
		In this example, a° and b° are vertical angles.
		Angles a° and c° are also vertical angles (and must be equal), which means they are 140° each.
		Note: They are also called Vertically Opposite Angles, which is just a more exact way of saying the same thing.
	www.mathsisfun.com /geometry/vertical-angles.html (148 words)

	Measuring Zenith & Vertical Angles
		Angles in the vertical plane are designated as either:
		A theodolite equipped with a vertical circle level bubble has 0 on the vertical circle oriented toward the zenith.
		Calculate (a) the corrected zenith angle and (b) the corrected vertical angle.
	www.emba.uvm.edu /~asadek/lect17.htm (295 words)

	Exploration Guide: Investigating Angle Theorems - Activity A Gizmo \| ExploreLearning
		Angles that share a vertex and have a common side but no common interior points are called adjacent angles.
		Vertical angles are pairs of angles that are formed by intersecting lines and are opposite each other.
		Turn on Show angle measures and use the protractor to confirm that the angles are complementary.
	www.explorelearning.com /index.cfm?method=cResource.dspExpGuide&ResourceID=282 (500 words)

	GMAT Geometry Chapter 2: Intersecting Angles
		In this case, the angles opposite one another are called vertical angles.
		As you can see, vertical angles are by definition always equal to each other.
		There are many terms from geometry class you may know to describe these angles, such as “alternate interior” or “alternate exterior,” but these terms are not used on the test.
	www.800score.com /guide7b1.html (378 words)

	Lesson and Concept attainment (Site not responding. Last check: 2007-10-25)
		With this information base, define vertical angles as: Angles that are opposite each other when 2 or more lines intersect at one point.
		Since 3 and 1 are vertical angles, this proves that vertical angles are congruent
		Write a description as to how we found out what vertical angles are and how we found out that vertical angles are congruent.
	www.mste.uiuc.edu /courses/ci399TSMsu02/students/dbechtel/lessonplans/Lesson6-13/Lesson_6-13.html (434 words)

	DryFire Laser Target Simulators to Determine Shotgun Leads and Angles
		The key factor is the angle between the clay and the aiming point.
		However, the lead angle you must allow is exactly the same as on the range.
		For a fast crosser that lead angle will be much larger than for a slow quartering target flying away from you.
	www.uslink.net /~dmeining/lead.htm (470 words)

	Angles with same vertex and vertical angles - free geometry lesson plan from Homeschool Math.net
		The two angles DAC and CAB have the same vertex point A. The angle DAB is a straight angle, thereby measuring __________ degrees.
		Measure all the angles in the pictures, including if there are any straight angles, and mark them on the pictures.
		These four angles are formed by two lines that intersect or cross each other at one point, A. Measure the angles DAC and EAB.
	www.homeschoolmath.net /teaching/g/same_vertex.php (475 words)

	Math Forum - Ask Dr. Math
		You must know that "vertical angles" are equal (or "congruent," as they say).
		Corresponding angles are found when parallel lines are crossed with a transversal.
		Is PDX one of a pair of corresponding angles?
	mathforum.org /library/drmath/view/57785.html (352 words)

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