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3.4 Parallel and Perpendicular Lines
3.4 Parallel/Perpendicular Lines
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Objective: To determine whether two lines are parallel
3.4 Parallel/Perpendicular Lines
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Vocabulary: Converse Flow Proof 3.4 Parallel/Perpendicular Lines
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Solve it: 3.4 Parallel/Perpendicular Lines
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Converse A statement in the form “If…, then…” is called a conditional statement. If you work hard, then you will have good grades. When the “if” and “then” parts are switched, it is called the converse of the statement. If you have good grades, then you worked hard. 3.4 Parallel/Perpendicular Lines
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Converses of Postulates and Theorems
Converse of the Corresponding Angles Postulate: If two lines and a transversal form corresponding angles that are congruent, then the lines are parallel. 3.4 Parallel/Perpendicular Lines
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Converses of Postulates and Theorems
Which lines are parallel if m < 1 = m <2 ? Justify your answer. 3.4 Parallel/Perpendicular Lines
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Converses of Postulates
Since <1 and <2 are corresponding, and m<1 = m<2 Then Line a is parallel to Line b 3.4 Parallel/Perpendicular Lines
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Converses of Postulates and Theorems
Converse of Alternate Interior Angles Theorem: If two lines and a transversal form Alternate Interior Angles that are congruent, then the lines are parallel. 3.4 Parallel/Perpendicular Lines
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Converses of Postulates and Theorems
Converse of Same Side Interior Angles Postulate: If two lines and a transversal form Same Side Interior Angles that are supplementary (1800), then the lines are parallel. 3.4 Parallel/Perpendicular Lines
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Converses of Postulates and Theorems
Converse of Alternate Exterior Angles Theorem: If two lines and a transversal form Alternate Exterior Angles that are congruent, then the lines are parallel. 3.4 Parallel/Perpendicular Lines
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Identifying Parallel Lines
Which lines are parallel if 1 2? Justify your answer. Which lines are parallel if 6 7? Justify your answer. 3.4 Parallel/Perpendicular Lines
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Identifying Parallel Lines
1) If 1 2 and <1 is corresponding to a <2 then Line a is || to Line b. if 6 7 and < 6 is corresponding to < 7 then Line m is || to Line L 3.4 Parallel/Perpendicular Lines
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Using Algebra What is the value of x for which a ll b?
3.4 Parallel/Perpendicular Lines
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Using Algebra Solution
If a ll b, then (2x+9) and 111 are same side interior angles. Thus : (2x+9) = Complementary 2x+120 = Addition 2x = Subtraction x = Division 3.4 Parallel/Perpendicular Lines
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Using Flow Charts 3.4 Parallel/Perpendicular Lines
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Using Flow Charts Given Transitive Property
Vertical <‘s are congruent 3.4 Parallel/Perpendicular Lines
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Using Flow Charts 3.4 Parallel/Perpendicular Lines
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Using Flow Charts Given Transitive Property Or Corresponding
Vertical <‘s are congruent 3.4 Parallel/Perpendicular Lines
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Lesson Check 3.4 Parallel/Perpendicular Lines
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Identifying Parallel Lines
3.4 Parallel/Perpendicular Lines
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