1. 2.5 Reasoning with Properties of Algebra
David Raju
Woodstock School
25 March 2017

2. 2.5 Reasoning with Properties of Algebra
25 March 2017

3. 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 .
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4. Algebraic properties Page 105 Addition property Subtraction property
Multiplication property
Division property
Reflexive property
Symmetric property
Transitive property
Substitution property
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5. 25 March 2017

6. 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.
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7. Q 1: Writing Reasons Solve 5x – 18 = 3x +2 5x – 18 = 3x + 2
Given
Subtraction property
Addition property
Division property
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8. 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
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9. Q 3: Using properties in Real Life
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10. 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?
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11. a) Solving for r a = 220 – 10/7r a + 10/7 r = 220 10/7r = 220 – a
Given
Addition property
Subtraction property
Multiplication property
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12. 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
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13. 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.
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14. 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
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15. Assignment Page 109 Q 3,4 Q 6,9 Q 15,18 Q 21-25 Q 33 25 March 2017