2.4 Reasoning in Algebra 2011.pdf
2.4 Reasoning in Algebra 2011.pdf
2.4 Reasoning in Algebra 2011.pdf
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<strong>2.4</strong> <strong>Reason<strong>in</strong>g</strong> <strong>in</strong> <strong>Algebra</strong> 2011September 20, 201124 <strong>Reason<strong>in</strong>g</strong> <strong>in</strong> <strong>Algebra</strong>ObjectiveJustify steps <strong>in</strong> solv<strong>in</strong>g an equation.1
<strong>2.4</strong> <strong>Reason<strong>in</strong>g</strong> <strong>in</strong> <strong>Algebra</strong> 2011September 20, 2011Warmup:2
<strong>2.4</strong> <strong>Reason<strong>in</strong>g</strong> <strong>in</strong> <strong>Algebra</strong> 2011September 20, 2011In geometry you accept postulates and properties as true.You also use them as justification to prove other statements.3
<strong>2.4</strong> <strong>Reason<strong>in</strong>g</strong> <strong>in</strong> <strong>Algebra</strong> 2011September 20, 2011When solv<strong>in</strong>g an equation you can justify each step with a:Examples: Angle Addition Postulateor Segment Addition Postulatepostulate,property,or aExamples on previous page.def<strong>in</strong>ition.Check the back of your book.4
<strong>2.4</strong> <strong>Reason<strong>in</strong>g</strong> <strong>in</strong> <strong>Algebra</strong> 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
<strong>2.4</strong> <strong>Reason<strong>in</strong>g</strong> <strong>in</strong> <strong>Algebra</strong> 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
<strong>2.4</strong> <strong>Reason<strong>in</strong>g</strong> <strong>in</strong> <strong>Algebra</strong> 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 <strong>in</strong> any expression.7
<strong>2.4</strong> <strong>Reason<strong>in</strong>g</strong> <strong>in</strong> <strong>Algebra</strong> 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
<strong>2.4</strong> <strong>Reason<strong>in</strong>g</strong> <strong>in</strong> <strong>Algebra</strong> 2011September 20, 2011Homeworkpage 105﴾1 23, 43 48﴿9
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