2.5 Reasoning with Properties of Algebra

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Presentation transcript:

2.5 Reasoning with Properties of Algebra David Raju Woodstock School 25 March 2017 http://apcalculusbc.com

2.5 Reasoning with Properties of Algebra 25 March 2017 http://apcalculusbc.com

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 . 25 March 2017 http://apcalculusbc.com

Algebraic properties Page 105 Addition property Subtraction property Multiplication property Division property Reflexive property Symmetric property Transitive property Substitution property 25 March 2017 http://apcalculusbc.com

25 March 2017 http://apcalculusbc.com

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 4. 25 March 2017 http://apcalculusbc.com

Q 1: Writing Reasons Solve 5x – 18 = 3x +2 5x – 18 = 3x + 2 Given Subtraction property Addition property Division property 25 March 2017 http://apcalculusbc.com

Q 2: Writing Reasons Solve: 55z – 3(9z + 12)= – 64 Given Distributiveproperty Simplify Addition property Division property 55z – 3(9z + 12)= -64 55z – 27z – 36 = -64 28z – 36 = -64 28z = -28 z = -1 25 March 2017 http://apcalculusbc.com

Q 3: Using properties in Real Life 25 March 2017 http://apcalculusbc.com

Find the following: Solve the equation for r and write a reason for each step. Use the result to find the target heart rate for a 16-year old. 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? 25 March 2017 http://apcalculusbc.com

a) Solving for r a = 220 – 10/7r a + 10/7 r = 220 10/7r = 220 – a Given Addition property Subtraction property Multiplication property 25 March 2017 http://apcalculusbc.com

b. Using a = 16, the target rate is: Given Substitute 16 for a Simplify The target rate for a 16 year old is about 143 beats per minute 25 March 2017 http://apcalculusbc.com

c. Age Rate 20 140 30 133 40 126 50 119 60 112 From the table, the target heart rate appears to decrease as the person gets older. 25 March 2017 http://apcalculusbc.com

In the fig AB =CD Show that AC = BD Given Addition property Segment addition postulate Substitution property AB = CD AB + BC = BC + CD AC = AB + BC BD = BC + CD AC = BD 25 March 2017 http://apcalculusbc.com

Assignment Page 109 Q 3,4 Q 6,9 Q 15,18 Q 21-25 Q 33 25 March 2017 http://apcalculusbc.com