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Topic: Isosceles trapezoid

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Isosceles trapezium

Trapezoid

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Complex polygon

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	Untitled Document
		A trapezoid is a quadrilateral with at least one pair of parallel sides by one definition and by another a trapezoid has exactly one pair of parallel sides.
		The portion of the median contained between the diagonals of a trapezoid is equal in length to the difference between the bases of the trapezoid.
		The diagonals of an isosceles trapezoid are congruent.
	www.auburn.edu /~westbsk/write-up2/index.htm (576 words)

	Trapezoid - MSN Encarta
		Trapezoid, in plane geometry, quadrilateral (four-sided) figure with two parallel sides, or bases, of unequal length.
		The sides that are not parallel are called legs, and a line from the midpoint of one leg to the midpoint of the other is called the median; the multiplication of the altitude and the median yields the area of the trapezoid.
		When the legs of a trapezoid are of equal length, the figure is called an isosceles trapezoid.
	encarta.msn.com /encyclopedia_761569599/Trapezoid.html (104 words)

	Trapezoid (Site not responding. Last check: 2007-10-05)
		Trapezoid is a convex quadrilateral with exactly one pair of parallel sides.
		Altitude (or height) is the segment perpendicular to the bases, and median is the segment connecting the midpoints of the legs.
		Trapezoid with congruent legs is an isosceles trapezoid.
	www.gomath.com /htdocs/lesson/trapezoid_lesson1.htm (110 words)

	Trapezoid - Wikipedia, the free encyclopedia
		A trapezoid (in North America) or trapezium (in Britain and elsewhere) is a quadrilateral two of whose sides are parallel to each other.
		Another necessary and sufficient condition is that the diagonals cut each other in mutually the same ratio; this ratio is the same as that between the lengths of the parallel sides.
		The area of a trapezoid can be computed as the length of the midsegment, multiplied by the distance along a perpendicular line between the parallel sides.
	en.wikipedia.org /wiki/Trapezoid (493 words)

	[No title]
		Assignment 2: Investigation of area equations (quadproof.gsp) Trapezoid 0.5(b1+b2)h Parallelogram bh Rhombus 0.5(d1+d2) [diagonals] Kite 0.5(d1+d2) Using knowledge obtained in Assignment 1 encourage students to derive the formula for the remaining quadrilaterals given the formula for a trapezoid.
		Trapezoid: a quadrilateral with 1 pair of parallel sides.
		Isosceles Trapezoid: a trapezoid with congruent base angles congruent left and right sides.
	www.mste.uiuc.edu /courses/ci336sp04/folders/meiland/ci336_final.doc (590 words)

	Lesson Seeds ~ VSC 3.C.1.a ~ Mathematics Grade 7 ~ School Improvement in Maryland
		Connections between the properties of rectangles, trapezoids, and parallelograms should be made so that students will better understand the formulas used to determine the areas of these quadrilaterals.
		If the trapezoid is not isosceles, create a copy of the trapezoid, flip it, and join it to the end of the original trapezoid.
		Determine the area of the trapezoid by showing it as the composition of a rectangle and a triangle.
	www.mdk12.org /instruction/lessons/mathematics/grade7/3C1a.html (489 words)

	The diaonals of an isosceles trapezoid are congruent (Site not responding. Last check: 2007-10-05)
		The key insight into all properties of the isosceles trapezoid is its symmetry.
		Given AP and BP are equal, we have a larger isosceles triangle which has a mirror of symmetry bisecting the angle at P and right bisecting the base AD.
		However, the optimum definitions are inclusive (yes a rectangle is an isosceles trapezoid) and do not use phrases such as: the equal sides are not parallel.
	mathcentral.uregina.ca /QQ/database/QQ.09.04/daniel2.html (423 words)

	Arabic Parts
		A rectangle is simultaneously a parallelogram and an isosceles trapezoid.
		The isosceles trapezoid is an elegant concept that integrates many seemingly disparate astrological concepts, such as midpoints, antiscia and solstice points, Jonas birth control, Vedic tithi returns, the traditional aspect patterns of grand trines, grand crosses, mystic rectangles, and yods, and even the very popular composite chart that was introduced in the 20th century.
		The isosceles trapezoid was identified by the founder of the Hamburg school of astrology Alfred Witte.
	www.astrosoftware.com /arabicparts.htm (2298 words)

	Isosceles trapezoid - Wikipedia, the free encyclopedia
		An isosceles trapezoid (isosceles trapezium in British English) is a quadrilateral with a line of symmetry bisecting one pair of opposite sides, making it automatically a trapezoid.
		Also, the diagonals of an isosceles trapezoid are congruent and intersect at equal positions.
		The area of an isosceles trapezoid (or any trapezoid) is equal to the average of the bases times the height.
	en.wikipedia.org /wiki/Isosceles_trapezoid (188 words)

	Trapezoid (C)
		A trapezoid is a quadrilateral with one and only one pair of parallel sides.
		If the altitude of a trapezoid has length h and the bases have lengths B and b then the area of the trapezoid is
		The altitude of a trapezoid is equal to the length of the shorter base.
	www.uwm.edu /~ericskey/TANOTES/Geometry/node9.html (123 words)

	Isosceles trapezoid (Site not responding. Last check: 2007-10-05)
		Compare the four line segements on the same isosceles trapezoid.
		Use ruler and compass contructions, or use Geometer's sketchpad, to construct the line segment parallel to the bases of length a and b to divide the isosceles trapezoid into two similar trapezoids.
		Use ruler and compass contructions, or use Geometer's sketchpad, to construct the line segment parallel to the bases of length a and b to divide the isosceles trapezoid into two trapezoids having the same area.
	jwilson.coe.uga.edu /emt725/Isos.Trpzd/isos.trpzd.html (249 words)

	Lesson 5
		Lesson Introduction: I will draw an isosceles trapezoid, trapezoid and kite on the board (one at a time) and have the students copy it into their notebooks and observe it.
		If the legs of the trapezoid are congruent then the trapezoid is an isosceles trapezoid.
		The midsegment of a trapezoid is parallel to each base and its length is the average of the two bases.
	www.tcnj.edu /~misbahu2/lesson_5.htm (420 words)

	section13
		A trapezoid with two non-parallel sides of the same length is called an isosceles trapezoid.
		Therefore angles A and D of the trapezoid ABCD are equal.
		The midsegment of a trapezoid is equal to 7 inches.
	www.math.psu.edu /geom/koltsova/section13.html (479 words)

	The Trapezoid (Site not responding. Last check: 2007-10-05)
		The trapezoid is a quadrilateral with one pair of parallel sides.
		The area of the trapezoid is equal to the average of the bases times the height.
		The base angles in an isosceles trapezoid are equal in measurement.
	id.mind.net /~zona/mmts/geometrySection/commonShapes/trapezoid/trapezoid.html (102 words)

	Mathematics Calculus Homework Help
		A water trough is 10 m long and a cross-section has the shape of an isosceles trapezoid that is 30cm wide at the bottom, 80 cm wide at the top, and has a height of 50 cm.
		Problem #21 - A water trough is 10 m long and a cross-section has the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 80 cm wide at the top, and has height 50 cm.
		Applied Optimization for a trapezoid - A trough with trapezoidal cross sections is formed by turning up the edges of a 30 inch wide sheet of aluminum.
	www.brainmass.com /homeworkhelp/math/calculus/7697 (256 words)

	[No title] (Site not responding. Last check: 2007-10-05)
		The opposite angles of an Isosceles Trapezoid are Supplementary.
		A midsegment of a triangle is equal to third side and opposite the length of the third side.
		The midsegment of a trapezoid opposite to the base and equal in length to the trapezoid of the length of the bases.
	members.tripod.com /cc_chengchang/item/geometry_definition.doc (443 words)

	83.01.07: Geometric Shapes in Architecture
		The equal sides of the isosceles triangle are the legs and the third side is the base of the triangle.
		In an isosceles triangle, the angles opposite the equal sides are equal.
		The area of the trapezoid is equal to the sum of the areas of these three polygons.
	www.yale.edu /ynhti/curriculum/units/1983/1/83.01.07.x.html (3540 words)

	All Elementary Mathematics - Study Guide - Geometry - Parallelogram and trapezoid...
		Trapezoid is a quadrangle, two opposite sides of which are parallel (Fig.36).
		The segment EF, joining midpoints E and F of the lateral sides, is called a midline of a trapezoid.
		This property follows from the previous part, as triangle can be considered as a limit case (“degeneration”) of a trapezoid, when one of its bases transforms to a point.
	www.bymath.com /studyguide/geo/sec/geo8.htm (429 words)

	Math "B" Terms
		Two angles of an isosceles triangle whose vertices are the endpoints of the base of the triangle.
		Two angles whose vertices are the endpoints of a base of the trapezoid.
		The base angles on an isosceles trapezoid are congruent.
	www.themathlab.com /dictionary/bwords/bwords.htm (367 words)

	Exhibit 11
		In a trisosceles trapezoid in which the legs and base have equal lengths, the trapezoid's diagonals bisect the angles formed by the legs and the summit (for example, in the figure shown below,
		And in a trisosceles trapezoid in which the legs and summit have equal lengths, the trapezoid's diagonals bisect the angles formed by the legs and the base.
		(1) The measure of angle 1 is equal to the measure of angle 2 because, in an isosceles triangle (for example, triangle ABD) the angles that are opposite to the triangle's two equal-length sides have equal measures.
	www.geocities.com /scott956282743/exhibit11.htm (294 words)

	2001-2002 QUADRILATERALS
		Assignment: Study the properties of an isosceles trapezoid.
		In a trapezoid, the length of one base is 5 times the length of the other base.
		The height of the trapezoid is 1 less than the length of the shorter base.
	www.fontbonne.org /Quads2.htm (123 words)

	An isosceles trapezoid (Site not responding. Last check: 2007-10-05)
		An isosceles trapezoid with bases of lengths 12 and 16 is inscribed in a circle with a radius of 10.
		The center of the circle lies in the interior of the trapezoid.
		C is the center of the circle and triangle ABC is a right triangle so you can use Pythagoras' theorem to find AC.
	mathcentral.uregina.ca /QQ/database/QQ.09.03/bruce3.html (85 words)

	Isosceles Trapezoid and JavaSketchpad
		the measurements of the angles of the isosceles trapezoid.
		the measurements of the sides of the isosceles trapezoid.
		the measurements of the diagonals of the isosceles trapezoid.
	regentsprep.org /Regents/math/quad/JavaTrapezoid.htm (72 words)

	High School Problems Archive (Site not responding. Last check: 2007-10-05)
		The bases of an isosceles trapezoid are 17 cm and 25 cm, and its base angles are 45°.
		Using the figure, the trapezoid is partitioned into two right triangles surrounding a rectangle.
		Since the triangles are isosceles right triangles with base angles of 45°, we see that each triangle's height, which is the trapezoid's height, is 4 cm.
	www.nctm.org /high/asolutions.asp?ID=81 (133 words)

	SparkNotes: Geometric Theorems: Terms
		Isosceles Trapezoid - A trapezoid with congruent legs.
		Lower Base Angles - The angles in an isosceles trapezoid whose vertices are the endpoints of the longer base.
		Upper Base Angles - The two angles of an isosceles trapezoid whose vertices are the endpoints of the smaller base.
	www.sparknotes.com /math/geometry2/theorems/terms.html (407 words)

	Selected Review Problems for Exam 1
		Only one pair of sides may be parallel in a trapezoid (the bases).
		Since this triangle is isosceles, the two base angles must be congruent (i.e.
		The square is both a rectangle and a kite (and a rhombus to boot).
	www.msu.edu /~hwangste/classes/mth202a/revexam1.html (785 words)

	Symmetry and Polygons
		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.
		In a trapezoid, consecutive angles between pairs of parallel sides are supplementary.
		In an isosceles trapezoid, the perpendicular bisector of one base is also the other base's perpendicular bisector.
	www.andrews.edu /~calkins/math/webtexts/geom06.htm (2551 words)

	Previous Questions
		Given: Isosceles Trapezoid ABCD where Segment AD is congruent to Segment BC and Segment AB is parallel to Segment CD Prove: Angle D is congruent to Angle C
		Given: Isosceles Trapezoid ABCD where Segment AD is congruent to Segment BC and Segment AB is parallel to Segment CD Prove: Segment AC is congruent to Segment BD Statements:
		Given: Isosceles Trapezoid ABCD where Segment AD is congruent to Segment BC and Segment AB is parallel to Segment CD Prove: Angle A is supplementary to Angle D
	www.gomath.com /Questions/question.php?question=42511 (553 words)

	Geometry Lesson 1-5 Instruction, last page
		In a trapezoid, at least one pair of opposite sides are parallel (Figure 1.26).
		The parallel sides are called the bases and the non-parallel sides are called the legs of the trapezoid.
		If in trapezoid the legs are congruent, it is called an isosceles trapezoid.
	www.etap.org /demo/geo1/instructiontutor_last.html (537 words)

	Chapter Two (Site not responding. Last check: 2007-10-05)
		A trapezoid is a quadrilateral with exactly one pair of parallel sides, the bases.
		An altitude of a trapezoid is a perpendicular segment from one base to the line containing the other base.
		Its length is called the height of the trapezoid.
	pages.cthome.net /jfleary/2gnf4/2gn4c6/2gn4(6-5).htm (78 words)

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