1. 3.3 Proving Lines Parallel
3.3 Proving Lines are Parallel

2. Objective: To determine whether two lines are parallel
3.3 Proving Lines are Parallel

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

4. Solve it:
3.3 Proving Lines are Parallel

5. 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

6. 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

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

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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
3.3 Proving Lines are Parallel

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

15. 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
3.3 Proving Lines are Parallel

16. Using Flow Charts
3.3 Proving Lines are Parallel

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

18. Using Flow Charts
3.3 Proving Lines are Parallel

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

20. Lesson Check
3.3 Proving Lines are Parallel

21. Identifying Parallel Lines
3.3 Proving Lines are Parallel