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David Raju Woodstock School 11 November 2013http://apcalculusbc.com

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2.5 Reasoning with Properties of Algebra 11 November 2013http://apcalculusbc.com

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Standards/Objectives: Standard 3: Students will learn and apply geometric concepts. Objectives: Use properties from Algebra Use properties of length and measure to justify segment and angle relationships, such as the angles at the turns of a racetrack. Use algebraic properties in logical arguments. 11 November 2013http://apcalculusbc.com

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Algebraic properties Page 105 Addition property Subtraction property Multiplication property Division property Reflexive property Symmetric property Transitive property Substitution property 11 November 2013http://apcalculusbc.com

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11 November 2013http://apcalculusbc.com

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Distributive Property a (b + c) = ab + ac Can be used to solve equations Example: x + 3 = 7 By subtracting 3 from each side of the equation, you obtain November 2013http://apcalculusbc.com

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Q 1: Writing Reasons Solve 5x – 18 = 3x x – 18 = 3x x – 18 = x = x = Given 2. Subtraction property 3. Addition property 4. Division property 11 November 2013http://apcalculusbc.com

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Q 2: Writing Reasons 1. 55z – 3(9z + 12)= z – 27z – 36 = z – 36 = z = z = Given 2. Distributiveproperty 3. Simplify 4. Addition property 5. Division property 11 November 2013http://apcalculusbc.com Solve: 55z – 3(9z + 12)= – 64

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Q 3: Using properties in Real Life 11 November 2013http://apcalculusbc.com

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Find the following: a. Solve the equation for r and write a reason for each step. b. Use the result to find the target heart rate for a 16- year old. c. Find the target rate for the following ages: 20, 30, 40, 50, and 60. What happens to the target heart rate as a person gets older? 11 November 2013http://apcalculusbc.com

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1. a = 220 – 10/7r 2. a + 10/7 r = /7r = 220 – a 4. r = 7/10(220 – a) 1. Given 2. Addition property 3. Subtraction property 4. Multiplication property 11 November 2013http://apcalculusbc.com a) Solving for r

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b. Using a = 16, the target rate is: 1. r = 7/10(220 – a) 2. r = 7/10(220 – 16) 3. r = Given 2. Substitute 16 for a 3. Simplify 11 November 2013http://apcalculusbc.com The target rate for a 16 year old is about 143 beats per minute

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c. AgeRate From the table, the target heart rate appears to decrease as the person gets older. 11 November 2013http://apcalculusbc.com

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In the fig AB =CD Show that AC = BD 1. AB = CD 2. AB + BC = BC + CD 3. AC = AB + BC 4. BD = BC + CD 5. AC = BD 1. Given 2. Addition property 3. Segment addition postulate 4. Segment addition postulate 5. Substitution property 11 November 2013http://apcalculusbc.com

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Assignment Page Q 3,4 2. Q 6,9 3. Q 15,18 4. Q Q November 2013http://apcalculusbc.com

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