David Raju Woodstock School 11 November 2013.

David RajuWoodstock School

April 10, 2023 http://apcalculusbc.com

2.5 Reasoning with Properties of Algebra


Standards/Objectives:Standard 3: Students will learn and apply geometric

concepts.

Objectives:Use properties from AlgebraUse 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 .


Algebraic propertiesPage 105

Addition propertySubtraction propertyMultiplication propertyDivision propertyReflexive propertySymmetric propertyTransitive propertySubstitution property


Distributive Propertya (b + c) = ab + acCan be used to solve equationsExample:

x + 3 = 7 By subtracting 3 from each side of the equation, you obtain 4.


Q 1: Writing ReasonsSolve 5x – 18 = 3x +21. 5x – 18 = 3x + 22. 2x – 18 = 23. 2x = 204. x = 10

1. Given2. Subtraction property3. Addition property4. Division property


Q 2: Writing Reasons

1. 55z – 3(9z + 12)= -64

2. 55z – 27z – 36 = -64

3. 28z – 36 = -64

4. 28z = -28

5. z = -1

1. Given

2. Distributiveproperty

3. Simplify

4. Addition property

5. Division property


Solve: 55z – 3(9z + 12)= – 64

Q 3: Using properties in Real Life


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?


1. a = 220 – 10/7r

2. a + 10/7 r = 220

3. 10/7r = 220 – a

4. r = 7/10(220 – a)

1. Given

2. Addition property

3. Subtraction property

4. Multiplication property


a) Solving for r

b. Using a = 16, the target rate is:1. r = 7/10(220 – a)

2. r = 7/10(220 – 16)

3. r = 142.8

1. Given

2. Substitute 16 for a

3. Simplify


The target rate for a 16 year old is about 143 beats per minute

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.


In the fig AB =CDShow that AC = BD

1. AB = CD2. AB + BC = BC + CD3. AC = AB + BC

4. BD = BC + CD

5. AC = BD

1. Given2. Addition property3. Segment addition

postulate4. Segment addition

postulate5. Substitution

property


Assignment

Page 1091.Q 3,42.Q 6,93.Q 15,184.Q 21-255.Q 33


David Raju Woodstock School 11 November 2013.

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