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Topic: Isosceles triangle

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	Triangle - Wikipedia, the free encyclopedia
		A perpendicular bisector of a triangle is a straight line passing through the midpoint of a side and being perpendicular to it, i.e.
		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.
		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.
	en.wikipedia.org /wiki/Isosceles_triangle (2072 words)

	TRIANGLE - LoveToKnow Article on TRIANGLE (Site not responding. Last check: 2007-11-06)
		The three sides and angles constitute the six elements of a triangle; it is customary to denote the angular points by capital letters and refer to the angles by these symbols; the sides are usually denoted by the lower case letter corresponding to that of the opposite angular point.
		The angles at the base of an isosceles triangle are equal and conversely; hence it follows that an equilateral triangle is also equiangular and conversely (i.
		We may here notice that the perpendiculars from the vertices of a triangle to the opposite sides are concurrent; their meet is called the orthocentre, and the triangle obtained by joining the feet of the perpendiculars is called the pedal triangle.
	80.1911encyclopedia.org /T/TR/TRIANGLE.htm (970 words)

	PlanetMath: triangle
		Triangles can be classified according to the number of their equal sides.
		So, a triangle with 3 equal sides is called equilateral, triangles with 2 equal sides are isosceles and finally a triangle with no equal sides is called scalene.
		Triangles can also be classified according to the size of the greatest of its three (inner) angles.
	planetmath.org /encyclopedia/Triangle.html (246 words)

	PlanetMath: isosceles triangle
		In any isosceles triangle, the angles opposite to the equal sides are also equal.
		In an equilateral triangle, the height, the median and the bisector to the third side are the same line.
		This is version 6 of isosceles triangle, born on 2001-10-06, modified 2004-03-17.
	planetmath.org /encyclopedia/IsoscelesTriangle.html (81 words)

	Figures and polygons
		The sum of the angles of a triangle is 180 degrees.
		The angles of an equilateral triangle all measure 60 degrees.
		One of the angles of the triangle measures 90 degrees.
	www.mathleague.com /help/geometry/polygons.htm (610 words)

	section5
		Finally, in a triangle ABC a segment that connects the vertex B and the middle point of the side opposite to the vertex B is called the median falling from the vertex B.
		Theorem 5.3 In an isosceles triangle a median falling from the vertex angle is also the bisector of the vertex angle and the altitude falling from the vertex angle.
		Triangles ACD and BCD are equal by SAS: AD = DB since D is the middle point of AB, AC = CB since the triangle ABC is an isosceles triangle and angles A and B are equal as base angles of an isosceles triangle ABC.
	www.math.psu.edu /geom/koltsova/section5.html (781 words)

	Tim's Triangular Page
		In an isosceles triangle, the median, bisectrix, and height of the vertext between the equal sides all coincide.
		Triangle DEF is congruent to triangles AFE, BFD, and CED.
		An isosceles triangle such that the ratio of the length of the two equal sides to the length of the third side is the golden ratio is called a golden triangle.
	sakharov.net /triangle.html (3567 words)

	AllRefer.com - triangle, in mathematics (Mathematics) - Encyclopedia
		In geometry it is shown that two triangles are congruent (i.e., are the same shape and size) if, in general, any three independent parts (sides or angles) of one are the same as the corresponding three parts of the other.
		The triangle is the simplest of the polygons (i.e., it has the least possible number of sides).
		Since any polygon can be broken up into triangles by drawing various diagonals, a complete theory of the measurement of triangles provides a complete theory of the measurement of all polygons.
	reference.allrefer.com /encyclopedia/T/triangl1.html (399 words)

	Math Online Q and A: Isosceles triangle ABC has vertices with coordinat (Site not responding. Last check: 2007-11-06)
		A centroid of a triangle is the point of concurrency of a triangle's medians.
		A triangle's median is the line segment with endpoints consisting of a vertex and the midpoint of the side opposite the vertex.
		In the case of your triangle with coordinates A(0,0), B(4,4), C(-3,7), the centroid is found at ((0 + 4 + -3)/3, (0 + 4 + 7)/3) or (1/3,11/3).
	www.mathonline.org /mho/view.cgi?13113 (398 words)

	Chapter Two
		The base angles of an isosceles triangle are the two angles formed by the base and one of the congruent sides.
		The vertex angle of an isosceles triangle is the angle formed by the congruent sides of the triangle.
		Theorem 4-4 Converse of the Isosceles Triangle Theorem
	pages.cthome.net /jfleary/2gnf4/2gn4c4/2gn4(4-5).htm (154 words)

	Session 5: Solutions
		The two shapes are congruent isosceles right triangles since all three pairs of corresponding sides are congruent, and two of the square's right angles are preserved, one in each triangle.
		The base of the triangle is half the length of the longer base of the trapezoid (midline theorem), and is of same length as the shorter base of the trapezoid.
		Form an isosceles triangle by flipping and translating triangle BEF so that angles A and E (the right angles) are adjacent and sides FA and EB align, thus forming a new shortest side of the new triangle.
	www.learner.org /channel/courses/learningmath/geometry/session5/solutions_homework.html (720 words)

	Program 1, COSC 143, Fall 2005 (Site not responding. Last check: 2007-11-06)
		An isosceles triangle is a triangle with (at least) two equal sides.
		An equilateral triangle is a triangle with three equal sides.
		In addition, if the triangle is isosceles, check to see if it is equilateral and if it is, say that it is -- again see sample run for specific output.
	www.uwplatt.edu /csse/courses/cs143/prog1.html (697 words)

	Isosceles triangles (Site not responding. Last check: 2007-11-06)
		The definition of an equilateral triangle is a triangle with three congruent sides.
		The definiton of an isosceles triangle is a triangle with at LEAST two congruent sides.
		Yes an equilateral triangle is an isosceles triangle - for each of the three possible pairs of sides.
	mathcentral.uregina.ca /QQ/database/QQ.09.99/amber1.html (440 words)

	Relations and sizes - Right triangle facts - In Depth (Site not responding. Last check: 2007-11-06)
		This version of the right triangle is so popular that plastic models of them are manufactured and used by architects, engineers, carpenters, and graphic artists in their design and construction work.
		The ratio of this triangle's longest side to its shortest side is "two to one." That is, the longest side is twice as long as the shortest side.
		He proved that, for a right triangle, the sum of the squares of the two sides that join at a right angle equals the square of the third side.
	www.math.com /school/subject3/lessons/S3U3L4DP.html (505 words)

	CS101 Lab no (Site not responding. Last check: 2007-11-06)
		An isosceles triangle has two equal sides and its third side is different from the equal sides.
		A right-angled triangle is a triangle where the square of a side is equal to the sum of the squares of the other two sides.
		If the given three numbers cannot be sides of a triangle (a side must be greater than 0, and summation of any two sides must be greater than other side), your program should print a message indicating this.
	www.cs.bilkent.edu.tr /~ilyas/Courses/cs101/lab06.html (281 words)

	essay1 (Site not responding. Last check: 2007-11-06)
		Given an isosceles triangle ABC with AB = AC and the measure of angle BAC = 100.
		Since the sum of the measure of the interior angles of all triangles must be 180, the measure of angles ABC and BCA must both be 40.
		Since the sum of the measure of the interior angles of all triangles must be 180, the measure of angles BEA and EAB must both be 40.
	jwilson.coe.uga.edu /EMT668/EMAT6680.F99/Wise/essay1/essay1.htm (537 words)

	PinkMonkey.com Geometry Study Guide - 2.3 Types of triangles
		Isosceles triangle : If only two sides of a triangle are equal in length, it is called as an isosceles triangle.
		A special case of an acute triangle is when all the three acute angles are equal.
		Obtuse triangle : A triangle in which one of the angles is obtuse is called as an obtuse triangle.
	www.pinkmonkey.com /studyguides/subjects/geometry/chap2/g0202301.asp (274 words)

	Higher Order Thinking Skills ~ VSC 2.A.2.a ~ Mathematics Grade 6 ~ School Improvement in Maryland
		Two isosceles triangles may not have the same side measures or angle measures.
		Two isosceles triangles may not have the same size or shape.
		If the sides of two equilateral triangles are the same, the triangles have the same size and are congruent.
	www.mdk12.org /instruction/thinking_skills/mathematics/grade6/2A2a.html (319 words)

	Triangles
		A triangle has three sides and is made of straight lines.
		A triangle may be classified by how many of its sides are of equal length.
		An acute triangle may be equilateral, isosceles, or scalene.
	www.factmonster.com /ipka/A0876325.html (164 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-11-06)
		Date: 11/6/96 From: Michelle Subject: Geometry Given that one base angle of an isosceles triangle is 39 degrees, find the measure of the other two angles in the triangle.
		As isosceles triangle has two congruent sides with a third side that is the base.
		A base angle of an isosceles triangle is one of the angles formed by the base and another side.
	mathforum.org /library/drmath/view/57753.html (310 words)

	The Triangle Figure
		When she placed an acute scalene triangle next to me on her desk, I remembered times as a student that I was asked to sketch an acute scalene triangle to investigate some triangle property.
		Any triangle in a pencil of triangles can be referred to by its third vertex, the one not incident with the base of the pencil.
		These two reflections may be used to generate a total of four congruent triangles within the same pencil, as long as the third vertex of the initial triangle is not on either of the lines of reflection.
	www.math.clemson.edu /~rsimms/triangle (1573 words)

	Ken's POTW 981201 (Site not responding. Last check: 2007-11-06)
		You are given an isosceles triangle ABC with side AB=AC, and angle BAC = 20 degrees.
		As ABC is isosceles with AB = AC, angle DBC = (180 - 20)/2 = 80° Let F on AC such as angle CBF = 20°.BCF is isosceles as ABC with BF = BC = a.
		In triangle FHE angle(HFE)=80=angle(CFE), angle(FHE)=70==> angle(FEH)=30=angle(FEO) In FOED angle(FDO)=30=angle(FEO)==>FOED is a cyclic quadrilateral (b) (a) ==> angle(OFC)=angle(OBC)=60 and angle(CFE)=80 ==>angle(OFE)=20 (b)==>angle(ODE)=angle(OFE)=20 ==> angle(CDE)=20
	www.ecst.csuchico.edu /~kend/potw/archive/981201sol.html (388 words)

	Isosceles - tribe.net
		The triangle is the strongest shape known to human kind.
		A triangle, which is perfectly formed and balanced on all sides can support a very large amount weight, yet remain small in size.
		Isosceles is a triangle that has two equal sides and one side that is unequal.
	isosceles.tribe.net (188 words)

	Symmetry and Polygons
		Triangles, as mentioned in Numbers lesson 11 and Geometry lesson 2, can be classified either by the number of sides with the same length (0 is scalene, 2 or more is isosceles, all 3 is equilateral) or by the largest angle (acute, right, obtuse).
		In an isosceles triangle, the bisector of the vertex angle,
		Although the line of symmetry of an isosceles triangle is an angle bisector, median, perpendicular bisector, and an altitude, in most triangles, these lines are different.
	www.andrews.edu /~calkins/math/webtexts/geom06.htm (2449 words)

	Topics in trigonometry: The isosceles right triangle
		Note that since the triangle is isosceles, then the angles at the base are equal.
		In the triangle on the left, the side corresponding to 1 has been multiplied by 6.5.
		Whenever we know the ratio numbers, we use this method of similar figures to solve the triangle, and not the trigonometric Table.
	www.themathpage.com /aTrig/isosceles-right-triangle.htm (313 words)

	AREA THE PENTAGRAM (Site not responding. Last check: 2007-11-06)
		In the figure to the left the area of the regular pentagon can be found by multiplying the area of the yellow isosceles triangle by 5.
		Therefore, we will subtract from the area of the pentagon 5 times the area of the red isosceles triangle, leaving the area of the pentagram.
		is the angle formed by the base and one of the two equal sides of the isosceles triangle.
	www.contracosta.cc.ca.us /math/stararea.htm (315 words)

	Does isosceles subsume equilateral? \| Ask MetaFilter
		My daughter was given homework in which she had to identify isosceles triangles.
		Mathworld says that an equilateral triangle is a special case of an isosceles triangle.
		Of trilateral figures, an equilateral triangle is that which has its three sides equal, an isosceles triangle that which has two of its sides alone equal, and a scalene triangle that which has its three sides unequal.
	ask.metafilter.com /mefi/15865 (1336 words)

	Isosceles triangle enigma (Site not responding. Last check: 2007-11-06)
		The problem is: given a diagram that looks like an isosceles triangle the segments that are formed by the two "base" angle bisectors and the sides opposite the angles are given to be congruent in length.
		Given only that these segments, which happen to bisect these angles and terminate on the legs, are equal in length--prove that the triangle is indeed isosceles.
		However, using trigonometry it is pretty simple: apply the Law of Sines to the two triangles formed by the angle bisectors and the apex of the main triangle.
	www.newton.dep.anl.gov /newton/askasci/1995/math/MATH083.HTM (207 words)

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