Warm Up

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Warm Up Solve each equation. 1. 3x 5 17 2.
r 3.5 8.7 3. 4t 7 8t 3 4. 5. 2(y 5)
20 0
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Objectives
Review properties of equality and use them to
write algebraic proofs. Identify properties of
equality and congruence.
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A proof is an argument that uses logic,
definitions, properties, and previously proven
statements to show that a conclusion is true.
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Property General Rule Example
Additive Identity
Multiplicative Identity
Multiplication Property of Zero
Multiplicative Inverse
Addition Property of Equality
Multiplication Property of Equality
Division Property of Equality
Subtraction Property of Equality
Reflexive Property of Equality
Symmetric Property of Equality
Transitive Property of Equality
Substitution Property of Equality
Distributive Property
Commutative Property of Addition
Commutative Property of Multiplication
Associative Property of Addition
Associative Property of Multiplication
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Example Identifying Property of Equality and
Congruence
Identify the property that justifies each
statement. A. ?QRS ? ?QRS B. m?1 m?2 so m?2
m?1 C. AB ? CD and CD ? EF, so AB ? EF. D. 32
32
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Example Solving an Equation in Algebra
Solve the equation 4m 8 12. Write a
justification for each step.
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Example 2 Problem-Solving Application
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Example Solving an Equation in Geometry
Write a justification for each step.
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Write a justification for each step.
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Lesson Quiz Part I
Solve each equation. Write a justification for
each step. 1.
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Lesson Quiz Part II
Solve each equation. Write a justification for
each step. 2. 6r 3 2(r 1)
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Lesson Quiz Part III
Identify the property that justifies each
statement. 3. x y and y z, so x z. 4. ?DEF
? ?DEF 5. AB ? CD, so CD ? AB.