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Topic: Transitive property of equality

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Transitive relation

Mathematics

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	Mathwords: Transitive Property of Equality
		Note: This is a property of equality and inequalities.
		One must be cautious, however, when attempting to develop arguments using the transitive property in other settings.
		Reflexive property of equality, symmetric property of equality, transitive property of inequalities, inequality rules
	www.mathwords.com /t/transitive_property.htm (94 words)

	Feature Synopsis for OWL Lite and OWL
		A property on a particular class may have a local range restriction associated with it.
		A particular class may have a restriction on a property that at least one value for that property is of a certain type.
		For example, the property has Offspring may have a minimum cardinality of zero on the class person (while it is stated to have the more specific information of minimum cardinality of one on the class parent).
	www.w3.org /TR/2002/WD-owl-features-20020729 (3894 words)

	Properties of Equality
		Transitive Property: Two numbers equal to the same or equal numbers are equal to each other.
		Roots Property: The absolute values of equal roots of equal positive numbers are equal.
		of consecutive angles the sum of whose measures equals the measure of the given angle
	home.xnet.com /~fidler/triton/math/review/mat075/reason/equal1.htm (213 words)

	[No title]
		property: terms that are to be used as relationships between individuals and classes may be defined as properties.
		If a property is symmetric, then if the pair (x,y) is an instance of the symmetric property P, then the pair (y,x) is also an instance of P. For example, friend may be stated to be a symmetric property.
		This allows the property hasOffspring to be used with other classes, possibly the class Cat and have an appropriate value restriction associated with the use of the property on that class.
	www.ksl.stanford.edu /people/dlm/webont/complianceMay262002.html (2885 words)

	Supplement to Algebra Textbooks
		A property or relationship is transitive if and only if in every case, whenever one thing has that relationship to a second thing, and the second thing has that relationship to a third thing, the first thing logically has to have that relationship to the third thing also.
		Being "a cousin of" is not transitive because not all the cousins of your cousins are cousins to you.
		Being "equal to" is reflexive, symmetrical, and transitive since everything is equal to itself (reflexive), equal to whatever is equal to it (symmetrical), and equal to anything equal to anything equal to it (transitive).
	www.garlikov.com /math/algebra.html (3071 words)

	Illuminations: Everything Balances Out in the End
		This property may also be demonstrated with with a pan balance in the classroom, placing 3 blue blocks in the left pan, and 3 blue blocks in the right pan.
		To develop kinesthetic understanding of the Reflexive Property of Equality, have students hold 3 cubes in their left hand, and 3 cubes in their right hand.
		Apply the properties of equality to solve traditional algebraic equations with algebra tiles using the handout, Balancing Equations.
	illuminations.nctm.org /LessonDetail.aspx?ID=L642 (1463 words)

	Properties of Equality (Site not responding. Last check: )
		When two quantities are equal, if you add the same number to both quantities, the sums will also be equal.
		When two quantities are equal, if you subtract the same number from both quantities, the differences will also be equal.
		When two quantities are equal, if they are divided by the same non-zero number, the quotients are also equal.
	www.gateways2learning.com /Algebra/EqualityProps.htm (86 words)

	The Mental Edge® - High School Geometry
		If two corresponding sides of two triangles are equal but the included angles are not equal, then the third side of the larger triangle is longer than the third side of the smaller triangle; and the included angle of the larger triangle is larger than the included angle of the smaller triangle.
		The measure of an exterior angle of a triangle is equal to the sum of its remote interior angles of the triangle.
		In a right triangle if the length of one leg and the length of the hypotenuse are known, then the length of the other leg is equal to the square root of the difference of the square of the hypotenuse and the square of the known leg.
	www.learningshortcuts.com /reviews/crsnd3.html (4096 words)

	Algebraic formulas
		This states that if two numbers are equal, they will remain equal if the same number is added or subtracted from them.
		*Property of inverse functions: Suppose f and f^-1 are inverse functions.
		Quotient property* of logarithms: For all positive numbers m, n, and b, where b is not equal to one, log b m/n = log b m – log b n.
	ks.essortment.com /pythagoreantheo_rnxu.htm (1724 words)

	Math Forum: Ask Dr. Math FAQ: Glossary of Properties
		Subtraction is not commutative: 2 - 1 is not equal to 1 - 2.
		The equals sign in an equation is like a scale: both sides, left and right, must be the same in order for the scale to stay in balance and the equation to be true.
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	www.mathforum.org /dr.math/faq/faq.property.glossary.html (836 words)

	[No title]
		For example, the property hasChild may be stated to have the domain of Mammal.
		For example, the property hasChild may be stated to have the range of Mammal.
		From this a reasoner may deduce that is X is related to Y by the property hasLeader, X is also related to Y by the property hasHead.
	www.ksl.stanford.edu /people/dlm/webont/complianceMay152002.html (3082 words)

	Feature Synopsis for OWL Lite and OWL
		Examples of properties would include: hasChild, hasRelative, hasSibling, hasAge, etc. The first three would be expected to relate an instance of a class person to another instance of the class person and the last one (hasAge) would be expected to relate an instance of the class person to an instance of the datatype Integer.
		For example, if the property P1 is stated to be the inverse of the property P2, then if X is related to Y by the P2 property, then Y is related to X by the P1 property.
		A minimum cardinality of zero on a property just states that (in the absence of any more specific information) that property is optional with respect to a class.
	www.ksl.stanford.edu /people/dlm/webont/OWLFeatureSynopsisJuly8.htm (4063 words)

	Feature Synopsis for OWL Lite and OWL
		A property on a particular class may have an existential local range restriction associated with it.
		That is, the restrictions limit the cardinality of that property on subclasses and instances of the class.
		Imports statements are transitive, that is, if ontology A imports B, and B imports C, then A imports both B and C. Importing an ontology into itself is considered a null action.
	www.ksl.stanford.edu /people/dlm/webont/OWLFeatureSynopsisJune23.htm (3697 words)

	Arithmetic Rules (Site not responding. Last check: )
		These are called the reflexive, symmetric, and transitive properties of equality.
		This definition consists of four axioms, called the identity, commutative, and associative properties of multiplication, and the distributive property of multiplication over addition.
		Then the distributive property is used, and finally x(-y) is subtracted from both sides.
	mcraeclan.com /MathHelp/BasicArithmetic.htm (1588 words)

	Math Forum - Ask Dr. Math
		In your example, I like the order it is in because most statements follow from the previous statement, possibly combined with an earlier one.
		AC = BD transitive property of equality (3,7) Everything still depends only on what came before, so it is a valid proof.
		Another point to make is that some people prefer to put all the givens as the first steps, rather than saving some for later, as in step 4 here.
	www.mathforum.com /dr.math/problems/crystal9.12.98.html (743 words)

	TrekFansUnited Forum > The Countdown (Site not responding. Last check: )
		The addition property of equality says that if a = b, then a + c = b + c: if you add the same number to (or subtract the same number from) both sides of an equation, the equation continues to be true.
		The multiplication property of equality says that if a = b, then a * c = b * c: if you multiply (or divide) by the same number on both sides of an equation, the equation continues to be true.
		The reflexive property of equality just says that a = a: anything is congruent to itself: the equals sign is like a mirror, and the image it "reflects" is the same as the original.
	www.trekfansunited.com /forum/lofiversion/index.php/t7515-700.html (2394 words)

	Other Number Properties
		And there are some properties that you use to solve word problems, especially where substitution is required.
		Anything equals itself: this is the "reflexive" (reflecting onto itself) property.
		You might be torn here between the transitive property and the substitution property.
	www.purplemath.com /modules/numbprop2.htm (607 words)

	Mathematical Proofs (Site not responding. Last check: )
		Clearly, if there is only one number in the set, as it is equal to itself (reflexive property of equality), all the numbers in this set are equal.
		But note that when we removed x from the set, y was still a member, and therefore equal to all the other members; and when we removed y from the set, we had replaced x, so it was a member equal to all the other members.
		Therefore x and y are both equal to all the other members of the set, so they must equal each other (transitive property of equality).
	my.voyager.net /~jayjo/proofs.htm (542 words)

	Algebra Postulates
		Dave didn't get a chance to write them, and I needed them for my section on the basic postulates of Geometry (review is always good).
		Transitive Property of Equality: if a = b and b = c, then a = c
		Substitution Property of Equality: if a = b, then a can be substituted for b in any equation or inequality
	library.thinkquest.org /2647/algebra/post.htm (303 words)

	sciforums.com - 1+1=?
		I suspect that most of the proof dealt with proving that 1+1 always equals the same thing.
		By the reflexive property of equality 4^0.5 = 4^0.5, but 4^0.5 could equal +2 or -2.
		This has to be the only way other than change of base that 1+1 may equal something other than 2.
	www.sciforums.com /showthread.php?p=789259 (764 words)

	ez2-3 & 2-4 Deductive Reasoning (Glencoe Geometry) (Site not responding. Last check: )
		For all numbers a, b, and c, if a = b, then a * c = b * c, and if c not equal to zero, a ÷ c = b ÷ c.
		These properties are used on a regular basis and are vital to the way that we work with numbers.
		In future sections we see how these same properties apply to segments, angles, etc...
	www.e-zgeometry.com /class/class2/2.3.4/2.3.4.htm (500 words)

	S.O.S. Mathematics CyberBoard :: View topic - [Resolved] Proofs
		When you are proving proofs in geometry, is it necessary to identify every single property along the way or can I skip over some small (non-important steps).
		Then I said that the vertical angles of 3 and 1, 2 and 4, and mequal because of the def.
		the book had the substitution property involved and transitive property involved which are understandable but not really necessary (at least I think).
	www.sosmath.com /CBB/viewtopic.php?t=1444 (387 words)

	The Reflexive Property of Equality states that any number is equal to itself (Site not responding. Last check: )
		The Reflexive Property of Equality states that any number is equal to itself
		This can be used when you have an equation with more than one variable, and you know the value of at least one variable.
		The distributive property is assumed to be true for subtraction.
	members.aol.com /teacherrs/principi.htm (458 words)

	Is The Creedal Doctrine Of The Trinity Biblical?
		By "trinity" I mean that within the nature of the one true God, there are three eternal, distinct Persons: the Father, the Son, and the Holy Spirit.
		By using the logical technique called the transitive property of equality (things equal to the same thing are equal to each other), I will now demonstrate the biblical doctrine of the Trinity.
		Therefore, as the transitive property of equality shows us, the three Persons Are the One God (Matthew 28:19).
	answers.org /theology/trinity_biblical.html (1544 words)

	Geometric Premises
		From this system of deductive logic you will build arguments to prove new conjectures based upon a collection of premises or accepted facts which in turn are based on given information or rules of congrunecy already established as fact.
		To begin builing a prior set of facts and premises you will first need to identify a few properties of Algebra, and then Properties of Equality.
		From the list of properties below, research, remember, find, or otherwise come up with a definition or example of the problem.
	powayusd.sdcoe.k12.ca.us /teachers/smiddleton/Geo/Proofs/Reasoning.htm (354 words)

	Activity, Curriculum, and Technology Lesson Plan
		Students will research from the links provided (links.doc) to get a better idea of what the properties mean and how they relate to the vocabulary words they were given.
		In the distributive property, you "distribute" the operation by multiplying the number outside of parenthesis to each number inside the parenthesis.
		Possible re-teaching and enrichment activities may include a presentation of projects, a warm-up activity in which the children would have to write a paragraph about how much better they understand the properties after the lesson, or a review or quiz activity.
	its.guilford.k12.nc.us /act/grade9_12/act9_12.asp?ID=662 (659 words)

	Chapter 2.1 Lesson, Math 101 - Fall 1997
		Eliminate fractions by multiplying both sides by the least common denominator.
		Combine like terms on each side of the equal sign.
		Use addition property of equality (maybe repeatedly) to get the equation into the form
	www.sci.wsu.edu /~kentler/Fall97_101/nojs/Chapter2/section1.html (251 words)

	Centers of a Triangle (Site not responding. Last check: )
		Since m is the perpendicular bisector of segment AC, DA =DC by the perpendicular bisector theorem.
		Thus DA=DB=DC, by the transitive property of equality.
		Since DB=DC, point D is on line n by the converse of the perpendicular bisector theorem.
	jwilson.coe.uga.edu /EMT668/EMAT6680.2003.Su/Glynn/4690A04.htm (301 words)

	Jiskha Homework Help - Mathematics: Arithmetic: Postulates
		Substitution Property of Equality: if a = b, then a can be substituted for b in any equation or inequality
		Transitive Property of Inequality: if a < b and b < c, then a < c
		Distributive Property: a * (b + c) = a * b + a * c and vice versa
	www.jiskha.com /mathematics/arithmetic/postulates.html (276 words)

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