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**2.5 Reasoning with Properties of Algebra**

David Raju Woodstock School 25 March 2017

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**2.5 Reasoning with Properties of Algebra**

25 March 2017

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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 . 25 March 2017

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**Algebraic properties Page 105 Addition property Subtraction property**

Multiplication property Division property Reflexive property Symmetric property Transitive property Substitution property 25 March 2017

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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 4. 25 March 2017

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**Q 1: Writing Reasons Solve 5x – 18 = 3x +2 5x – 18 = 3x + 2**

Given Subtraction property Addition property Division property 25 March 2017

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**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

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**Q 3: Using properties in Real Life**

25 March 2017

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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

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**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

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**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

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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

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**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

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**Assignment Page 109 Q 3,4 Q 6,9 Q 15,18 Q 21-25 Q 33 25 March 2017**

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Section 2.2 Day 1. A) Algebraic Properties of Equality Let a, b, and c be real numbers: 1) Addition Property – If a = b, then a + c = b + c Use them 2)

Section 2.2 Day 1. A) Algebraic Properties of Equality Let a, b, and c be real numbers: 1) Addition Property – If a = b, then a + c = b + c Use them 2)

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