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Sec 2-5 Concept: Reasoning with Properties from Algebra Objective: Given properties from Algebra, justify segment and angle relationships as measured by a s.g

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Example 1: Pay Raises. Suppose your receive a pay raise at work. You can calculate your percent increase by using the pay raise formula c(1+r) = n, where c is your current wage (in dollars per hour), r is your percent increase (as a decimal) and n is your new wage ( in dollars per hour) Solve the formula for r and write a reason for each step C(1+r) = nGiven c+cr = n Distributive Property -c -c cr = n-c Subtraction Property c c Division Property r = n-c c

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Example 1 cont.: Pay Raises. Suppose your receive a pay raise at work. You can calculate your percent increase by using the pay raise formula c(1+r) = n, where c is your current wage (in dollars per hour), r is your percent increase (as a decimal) and n is your new wage ( in dollars per hour) Use result from the previous page to find your percent increase if you current wage is $10.00 and your new wage will be $10.80 r = n-c c r= r=.08 or 8%

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Example 2: Use the property to complete the statement 1. Transitive Property of Equality: If BC=CD and CD = EF, then _______ BC = EF 2. Subtraction Property of Equality: If PQ+ST=RS+ST then, ________ PQ = RS

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Example 3: Solve the equation and state a reason for each step q+9 = 13 Given -9 Subtraction property q= 4

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Example 3cont: Solve the equation and state a reason for each step -2(-w+3)=15 Given 2w-6 =15 Addition Property Distributive Property 2w = Division Propery w = 10.5

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Example 4

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Example 5 Show that the perimeter of triangle ABC is equal to the perimeter of triangle ADC AD = CB DC=BA AC=AC AD+DC=CB+DC AD+DC=CB+BA AD+DC+AC=CB+BA+AC Equation: Reason: Explanation:

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Todays Work In Class: HW:

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