3 3 Proving Lines Parallel 3 3 Proving

3. 3 Proving Lines Parallel 3. 3 Proving Lines are Parallel

Objective: • To determine whether two lines are parallel 3. 3 Proving Lines are Parallel

Vocabulary: • Converse • Flow Proof 3. 3 Proving Lines are Parallel

Solve it: 3. 3 Proving Lines are Parallel

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. 3 Proving Lines are Parallel

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. 3 Proving Lines are Parallel

Converses of Postulates and Theorems Which lines are parallel if m < 1 = m <2 ? Justify your answer. 3. 3 Proving Lines are Parallel

Converses of Postulates Since <1 and <2 are corresponding, and m<1 = m<2 Then Line a is parallel to Line b 3. 3 Proving Lines are Parallel

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. 3 Proving Lines are Parallel

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. 3 Proving Lines are Parallel

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. 3 Proving Lines are Parallel

Identifying Parallel Lines • Which lines are parallel if 1 2? Justify your answer. • Which lines are parallel if 6 7? Justify your answer. 3. 3 Proving Lines are Parallel

Identifying Parallel Lines 1) If 1 2 and <1 is corresponding to a <2 then Line a is || to Line b. 2) if 6 7 and < 6 is corresponding to < 7 then Line m is || to Line L 3. 3 Proving Lines are Parallel

Using Algebra • What is the value of x for which a ll b? 3. 3 Proving Lines are Parallel

Using Algebra Solution • If a ll b, then (2 x+9) and 111 are same side interior angles. Thus : (2 x+9) + 111 = 180 2 x+120 = 180 2 x = 60 x = 30 Complementary Addition Subtraction Division 3. 3 Proving Lines are Parallel

Using Flow Charts 3. 3 Proving Lines are Parallel

Using Flow Charts Given Transitive Property Vertical <‘s are congruent 3. 3 Proving Lines are Parallel

Using Flow Charts 3. 3 Proving Lines are Parallel

Using Flow Charts Given Vertical <‘s are congruent Transitive Property Or Corresponding 3. 3 Proving Lines are Parallel

Lesson Check 3. 3 Proving Lines are Parallel

Identifying Parallel Lines 3. 3 Proving Lines are Parallel