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Topic: Altitude (triangle)

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  Geometry Forum Project of the Month - Jan. 1996
The altitudes of an acute triangle are in the interior of the triangle.
In an isosceles triangle, from the vertex angle, the altitudes are perpendicular bisectors and medians.
For an equilateral triangle, all the medians are congruent.
mathforum.org /pom/sols2.96.html   (7088 words)

 Triangle (geometry) - MSN Encarta
A capital letter is customarily used to designate a vertex of a triangle, the angle at that vertex, or the measure of the angle in angular units; the corresponding lower case letter designates the side opposite the angle or its length in linear units.
Therefore, the three angles of a scalene triangle are of different sizes; the base angles of an isosceles triangle are equal; and the three angles of an equilateral triangle are equal (an equilateral triangle is also equiangular).
For example, the sum of the angles of a spherical triangle is between 180° and 540° and varies with the size and shape of the triangle.
encarta.msn.com /encyclopedia_761563143/Triangle_(geometry).html   (811 words)

 Altitude - Biocrawler   (Site not responding. Last check: 2007-10-09)
Altitude is the elevation of an object from a known level or datum, called zero level.
In astronomy and surveying, altitude is one of the two coordinates of the horizontal coordinate system, and refers to the vertical angle from the horizon.
In geometry, an altitude of a triangle is a line passing through one vertex and being perpendicular to the opposite side.
www.biocrawler.com /encyclopedia/Altitude   (470 words)

 Altitude (triangle) - Wikipedia, the free encyclopedia
The length of the altitude is the distance between the base and the vertex.
The isogonal conjugate of the orthocenter is the circumcenter.
It is the pedal triangle of the orthocenter of the original triangle.
en.wikipedia.org /wiki/Altitude_(triangle)   (446 words)

 Triangle - Gurupedia
A central theorem is the Pythagorean theorem stating that in any right triangle, the area of the square on the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
A perpendicular bisector of a triangle is a straight line passing through the midpoint of a side and being perpendicular to it, i.e.
The area S of a triangle is S = ½bh, where b is the length of any side of the triangle (the base) and h (the altitude) is the perpendicular distance between the base and the vertex not on the base.
www.gurupedia.com /t/tr/triangle_(geometry).htm   (1679 words)

 Word Problems: Area and Perimeter of Triangles   (Site not responding. Last check: 2007-10-09)
We may also be given a relationship between the area and perimeter or between the sides and altitude of the triangle.
Suppose in a right triangle one of the legs is of length 5 and the angle formed by the hypotenuse and this leg is 28°.
There are formulas for an equilateral triangle that relate h to the length of a side and that relate the area to the length of a side.
www.algebralab.org /Word/Word.aspx?file=Geometry_AreaPerimeterTriangles.xml   (757 words)

 All about altitudes
An altitude is the portion of the line between the vertex and the foot of the perpendicular.
Thus, the fact that, in a triangle, angle bisectors are concurrent, implies the fact that altitudes in a triangle are also concurrent.
H is an angle bisector in the orthic triangle.
www.cut-the-knot.org /triangle/altitudes.shtml   (1368 words)

 Triangle - Wikipedia, the free encyclopedia
A triangle is one of the basic shapes of geometry: a polygon with three vertices and three sides which are straight line segments.
A median of a triangle is a straight line through a vertex and the midpoint of the opposite side, and divides the triangle into two equal areas.
Examples of non-planar triangles in noneuclidean geometries are spherical triangles in spherical geometry and hyperbolic triangles in hyperbolic geometry.
en.wikipedia.org /wiki/Triangle   (2234 words)

The orthocenter of a triangle is the point where the three altitudes meet.  This point may be inside, outside, or on the triangle.  Here are some properties of the orthocenter that I find to be interesting.
Of all the triangles that could be inscribed in a given triangle, the one with the smallest perimeter is the orthic triangle.
Fagnano also was the first to show that the altitudes of the original triangle are the angle bisectors of the orhtic triangle, so the incenter of the orthic triangle is the orthocenter of the original triangle.
www.pballew.net /orthocen.html   (1819 words)

 UFO.Whipnet.org | Aliens | UFO | Flying Triangle's on Rise
Kelleher said the analysis indicates that deployment of Flying Triangles is open, not covert, and involves low-flying, brightly lit aircraft routinely deployed over populated areas including cities and interstate highways.
While it is too early to dismiss the previously published NIDS correlation between Triangle sightings and a subset of U.S. Air Force bases, the apparent association with centers of population may point away from a covert program.
The sightings of Triangles appear primarily adjacent to population centers and along interstate highways, with sightings clustered on both coasts.
ufo.whipnet.org /xdocs/flying.triangle   (1176 words)

 Triangle definition - Math Open Reference
The vertex (plural: vertices) is a corner of the triangle.
The altitude of a triangle is the perpendicular from the base to the opposite vertex.
The median of a triangle is a line from a vertex to the midpoint of the opposite side.
www.mathopenref.com /triangle.html   (392 words)

 Mathwords: Altitude of a Triangle
The distance between a vertex of a triangle and the opposite side.
Altitude also refers to the length of this segment.
Note: The three altitudes of a triangle are concurrent, intersecting at the orthocenter.
www.mathwords.com /a/altitude_triangle.htm   (68 words)

 Altitude of a Triangle,Orthocenter
The distance between a vertex of a triangle and the opposite side is altitude.
Formally, the shortest line segment between a vertex of a triangle and the (possibly extended) opposite side.
For an obtuse triangle (having one angle exceeding 90°), the orthocenter lies outside the triangle, because the lines of the altitudes intersect in one point.
www.math10.com /en/geometry/altitude.html   (102 words)

 TRIANGLE MANIA   (Site not responding. Last check: 2007-10-09)
- An altitude is the line from a vertex of a triangle drawn perpendicular to the side opposite the vertex.
The corner points of the triangle are endpoints of the line segments.
- The perimeter of a triangle is the length of the distance around the outside of the triangle.
www.calstatela.edu /faculty/eviau/edit557/triangles/mary/glossary.html   (208 words)

 SparkNotes: Geometric Measurements: Terms and Formulae
Altitude of a Trapezoid - In a trapezoid, the segment with one endpoint on a base and perpendicular to that base, with the other endpoint on the line containing the other base.
Altitude of a Triangle - In a triangle, the segment with one endpoint on a vertex, and the other endpoint on the side opposite the vertex, and perpendicular to that side.
] - [(1/2)bh], where n is the measure of the arc in degrees, b is the measure of the base of the triangle formed by the radii and the chord, and h is the length of the altitude of that triangle.
www.sparknotes.com /math/geometry2/measurements/terms.html   (611 words)

 PinkMonkey.com Geometry Study Guide - 2.4 Altitude, Median and Angle Bisector
An altitude is a perpendicular dropped from one vertex to the side (or its extension) opposite to the vertex.
For an acute triangle figure 2.10 all the altitudes are present in the triangle.
Similarly seg.CE is altitude on to AB and BF is the altitude on to seg.
www.pinkmonkey.com /studyguides/subjects/geometry/chap2/g0202401.asp   (299 words)

 Right Triangle Median, Altitude, Bisector   (Site not responding. Last check: 2007-10-09)
Suppose triangle ABC is a right triangle, shown inscribed in a circle with diameter AB and center M. The bisector of angle ACB is shown here in purple, along with the perpendicular bisector of AB.
Law of Sines - Given triangle ABC with opposite sides a, b, and c, a/(sin A) = b/(sin B) = c/(sin C) = the diameter of the circumscribed circle.
Triangle Trisection -- If a point, P, on the median of triangle ABC is the isogonal conjugate of point Q, on the altitude of ABC, then ABC is a right triangle.
mcraefamily.com /MathHelp/GeometryTriangleRightMedianAndAltitudeAreReflectionsAboutBisector.htm   (386 words)

 5.1 Triangles
In an acute triangle all angles are acute.
The point of intersection of the medians is the center of mass of the triangle (considered as an area in the plane).
For an isosceles triangle, the altitude for the unequal side is also the corresponding bisector and median, but this is not true for the other two altitudes.
www.geom.uiuc.edu /docs/reference/CRC-formulas/node22.html   (704 words)

 Untitled Document   (Site not responding. Last check: 2007-10-09)
Then the class will discuss the Theorem 7.1 which states that: if the altitude drawn from the vertex of the right angle of a right triangle to its hypotenuse, then the two triangles formed are similar to the given triangle and to each other.
The students should know that the altitude of a triangle forms a right angle so in the case of the right triangle, the altitude would create two right triangles.
This activity would be used to give the students a better understanding of the relationship between triangles formed by the altitude of a right triangle.
www.auburn.edu /~scottaj/labexperience/altitudes.htm   (206 words)

 Triangle Trisection   (Site not responding. Last check: 2007-10-09)
In this question, angle A of a triangle is trisected, angle C is bisected, and BM is the triangle median.
If the median and altitude of triangle ABC are reflections about the bisector of B, as they are here, then ABC is a right triangle.
Proof that the median and altitude of a right triangle are reflections about the bisector iff ABC is a right triangle.
mcraefamily.com /mathhelp/GeometryTriangleTrisection.htm   (362 words)

 Math Forum - Ask Dr. Math   (Site not responding. Last check: 2007-10-09)
Date: 03/07/99 at 03:07:02 From: Michelle Cheung Subject: Altitude of a triangle In triangle PQR, angle Q is obtuse, PQ = 11, QR = 25, and PR = 30.
Date: 03/07/99 at 03:29:50 From: Doctor Pat Subject: Re: Altitude of a triangle You are given three sides of a triangle.
Since the altitude to PQ is requested, let PQ be the base.
mathforum.org /library/drmath/view/55099.html   (214 words)

 Area of a triangle (conventional method) - Math Open Reference
a is the length of the corresponding altitude
The altitude must be the one corresponding to the base you choose.
The altitude is the line perpendicular to the selected base from the opposite vertex.
www.mathopenref.com /trianglearea.html   (161 words)

 Triangle (C)   (Site not responding. Last check: 2007-10-09)
The perimeter of the triangle is the sum of the lengths of the sides.
What is the area of a triangle with one side of length 5 and altitude from that side equal to 4?
Find the length of the equal sides of an isosceles triangle if the area of the triangle is 5 and the remaining side has length 4.
www.uwm.edu /~ericskey/TANOTES/Geometry/node7.html   (147 words)

 Altitudes - GeoGebra Dynamic Worksheet   (Site not responding. Last check: 2007-10-09)
When a mathematician sees a behavior like this that works with all triangles (or at least with a bunch of examples that we have looked at) the suspicion is that there must be a structure that helps us prove that it must always happen.
With the initial triangle we construct a similar triangle of twice the size by tiling together 4 identical triangles.
the altitudes of the original triangle are the perpendicular bisectors of the larger triangle.
www.slu.edu /classes/maymk/GeoGebra/Altitudes.html   (221 words)

 Animated Angle to Geometry Problems and Theorems - Level: High School, SAT Prep, GRE, GMAT, College geometry. Cabri, ...
Triangle with the bisectors of the exterior angles.
Triangle with Squares 5 Two squares, median and altitude.
Here were assertions, as for example the intersection of the three altitudes of a triangle in one point, which - though by no means evident - could nevertheless be proved with such certainty that any doubt appeared to be out of the question.
agutie.homestead.com /files/Geoproblem_B.htm   (489 words)

 Error Analysis
The effect of base line length error on aircraft AGL altitude accuracy is directly proportional to the ratio of the (base length measurement error)/(base length).
The maximum aircraft altitude error for this example caused by the +/-.2 degree measurement error is +/- 7.1 feet.
The maximum total system error on the calculations of the aircraft altitude would be the addition of all the previous described errors.
lowflying.bizland.com /error_analysis.htm   (452 words)

 The Euler Line of a Triangle
An altitude of the triangle is a line drawn through a vertex perpendicular to the side of the triangle opposite the vertex.
Note that when the triangle is obtuse, two of the altitudes lie outside the triangle, so they actually connect a vertex to the opposite side extended.
Since the altitudes of the original triangle meet at the orthocenter H of the original triangle, the altitudes of the medial triangle will meet at its orthocenter H' which you can see in the figure is labelled O.
aleph0.clarku.edu /~djoyce/java/Geometry/eulerline.html   (929 words)

 Jadonna Brewton: EMAT6680/Fall2000/Assignment8
An altitude in a triangle is a perpendicular segment from a vertex to the side opposite that vertex.
Also, the intersection points (feet) of the altitudes and the sides of the triangle are labeled O, R, and T.
triangles is the orthocenter of the original triangle.
jwilson.coe.uga.edu /emt668/EMAT6680.2000/Brewton/brew08/writeup8.html   (149 words)

 SPACE.com -- Silent Running: 'Black Triangle' Sightings on the Rise
Based in Las Vegas, Nevada, NIDS is a privately funded science institute with a strong research focusing on aerial phenomena.The results of their study have just been released and lead to some unnerving, still puzzling conclusions.
According to Colm Kelleher, NIDS Administrator, the newly completed quasi “meta-analysis” of Flying Triangles melds three major U.S. databases: NIDS, the Mutual UFO Network (MUFON) and data collected by independent researcher, Larry Hatch, the creator and owner of one of the largest and most comprehensive UFO databases in the world.
The trend of open deployment of the Flying Triangles is not consistent with secret operation of an advanced DoD aircraft.
www.space.com /businesstechnology/flying_triangle_040902.html   (1327 words)

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