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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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**c+cr = n -c -c cr = n-c c c r = n-c c**

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) = n Given c+cr = n Distributive Property -c c cr = n-c Subtraction Property c c r = n-c c Division Property

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**Example 1 cont. : Pay Raises. Suppose your receive a pay raise at work**

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= 10.00 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**

Given q= 4 Subtraction property

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**Example 3cont: Solve the equation and state a reason for each step**

-2(-w+3)=15 Given 2w-6 =15 Distributive Property +6 +6 2w = 21 Addition Property w = 10.5 Division Propery

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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**

Reason: Equation: Explanation: AD = CB DC=BA AC=AC AD+DC=CB+DC AD+DC=CB+BA AD+DC+AC=CB+BA+AC

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Today’s Work In Class: HW:

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2.5 Reasoning and Algebra. Addition Property If A = B then A + C = B + C.

2.5 Reasoning and Algebra. Addition Property If A = B then A + C = B + C.

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