Lesson 2.5 Using Proof in Algebra

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Lesson 2.5 Using Proof in Algebra

• Properties page 97 99

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2.5 examples

• Name the property
• If 3x 120, then x 40
• If 12 AB, then AB 12
• If AB BC, and BC CD, then AB CD
• If y 75 and y m?A, then angle m? A 75

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Examples continued

• Justify each step
• Given
• ___________
• x -9 ____________

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EXAMPLE 1
Write reasons for each step
Solve 2x 5 20 3x. Write a reason for each
step.
2x 5 20 3x
Write original equation.
Given
2x 5 3x 20 3x 3x
Add 3x to each side.
Addition Property of Equality
5x 5 20
Combine like terms.
Simplify.
Subtract 5 from each side.
5x 15
Subtraction Property of Equality
x 3
Divide each side by 5.
Division Property of Equality
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EXAMPLE 1
Write reasons for each step
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EXAMPLE 2
Use the Distributive Property
Solve -4(11x 2) 80. Write a reason for each
step.
SOLUTION
4(11x 2) 80
Write original equation.
Given
44x 8 80
Multiply.
Distributive Property
44x 88
Add 8 to each side.
Addition Property of Equality
x 2
Divide each side by 44.
Division Property of Equality
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EXAMPLE 3
Use properties in the real world
Heart Rate
When you exercise, your target heart rate should
be between 50 to 70 of your maximum heart rate.
Your target heart rate r at 70 can be determined
by the formula r 0.70(220 a) where a
represents your age in years. Solve the formula
for a.
SOLUTION
Write original equation.
r 0.70(220 a)
Given
r 154 0.70a
Multiply.
Distributive Property
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EXAMPLE 3
Use properties in the real world
r 154 0.70a
Subtract 154 from each side.
Subtraction Property of Equality
Divide each side by 0.70.
Division Property of Equality
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for Examples 1, 2 and 3
GUIDED PRACTICE
In Exercises 1 and 2, solve the equation and
write a reason for each step.
1. 4x 9 3x 2
Write original equation.
4x 9 3x 2
Given
7x 9 2
Add 3x to each side.
Addition Property of Equality
Subtract 9 from each side.
Subtraction Property of Equality
7x 7
Divide each side by 7.
x 1
Division Property of Equality
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for Examples 1, 2 and 3
GUIDED PRACTICE
2. 14x 3(7 x) 1
14x 3(7 x) 1
Write original equation.
Given
14x 21 - 3x 1
Multiply.
Distributive Property
11x 21 1
Simplify
Link the same value
11x 22
Subtract 21 from each side.
Subtraction Property of Equality
x 2
Divide each side by 11.
Division Property of Equality
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for Examples 1, 2 and 3
GUIDED PRACTICE
Write original equation.
Given
Multiply
Multiplication property
Divide
Division property
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EXAMPLE 4
Use properties of equality
LOGO
SOLUTION
Marked in diagram.
Given
Add measures of adjacent angles.
Angle Addition Postulate
Substitution Property of Equality
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EXAMPLE 4
Use properties of equality
Add measures of adjacent angles.
Angle Addition Postulate
Transitive Property of Equality
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EXAMPLE 5
Use properties of equality
SOLUTION
Marked in diagram.
AB CD
Given
AC AB BC
Add lengths of adjacent segments.
Segment Addition Postulate
BD BC CD
Add lengths of adjacent segments.
Segment Addition Postulate
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EXAMPLE 5
Use properties of equality
Add BC to each side of AB CD.
AB BC CD BC
Addition Property of Equality
AC BD
Substitute AC for AB BC and BD for BC CD.
Substitution Property of Equality
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for Examples 4 and 5
GUIDED PRACTICE
Name the property of equality the statement
illustrates.
5. If JK KL and KL 12, then JK 12.
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for Examples 4 and 5
GUIDED PRACTICE
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Daily Homework Quiz
Solve. Give a reason for each step.
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Daily Homework Quiz
Solve. Give a reason for each step.
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Daily Homework Quiz
3.
If m 3 m 5 and m 5 m 8, then m
3 m 8.