2.4 Reasoning in Algebra 2011.pdf

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2.4 Reasoning in Algebra 2011.pdf

2.4 Reasoning in Algebra 2011September 20, 20112­4 Reasoning in AlgebraObjectiveJustify steps in solving an equation.1


2.4 Reasoning in Algebra 2011September 20, 2011Warm­up:2


2.4 Reasoning in Algebra 2011September 20, 2011In geometry you accept postulates and properties as true.You also use them as justification to prove other statements.3


2.4 Reasoning in Algebra 2011September 20, 2011When solving an equation you can justify each step with a:Examples: Angle Addition Postulateor Segment Addition Postulatepostulate,property,or aExamples on previous page.definition.Check the back of your book.4


2.4 Reasoning in Algebra 2011September 20, 2011Example #1: Solve for x and justify each step.Given: m AOC = 139AxB2x + 10OCStepsJustifications1. m AOB + m BOC = m AOC 1. Angle Addition Postulate2. x + 2x + 10 = 139 2. Substitution3. 3x + 10 = 139 3. Simplify4. 3x = 129 4. Subtraction Property of Equality5. x = 43 5. Division Property of Equality5


2.4 Reasoning in Algebra 2011September 20, 2011Example #2: Solve for y and justify each step.Given: AC = 21 2y 3y ­ 9A B CStepsJustifications1. AB + BC = AC 1. Segment Addition Postulate2. 2y + 3y ­ 9 = 21 2. Substitution Property3. 5y ­ 9 = 21 3. Simplify4. 5y = 30 4. Addition Property of Equality5. y = 6 5. Division Property of Equality6


2.4 Reasoning in Algebra 2011September 20, 2011Properties of CongruenceReflexive Propertya = aSymmetric Property If a = b, then b = a.Transitive Property If a = b and b = c, then a = c.Substitution PropertyIf a = b, then b can replace a in any expression.7


2.4 Reasoning in Algebra 2011September 20, 2011Name the property of congruence that justifies each statement.~1. K = KReflexive Property of Congruence~ ~ ~2. If RS = TW and TW = PQ, then RS = PQ.Transitive Property of Congruence3. If m A = m B, then m B = m A.Symmetric Property of Equality8


2.4 Reasoning in Algebra 2011September 20, 2011Homeworkpage 105﴾1 ­ 23, 43 ­ 48﴿9

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