1. Proving Lines Are Parallel
Chapter 3 Section 3.4
Proving Lines Are Parallel

2. Warm-Up State the converse of each statement.
If <1 is a right angle, then m<1=90
If m<1 = 90, then <1 is a right angle.
2. If m<1 + m<2=180,
then <1 and <2 are supplementary.
If <1 and <2 are supplementary,
then m<1 + m<2 = 180

3. When two lines are cut by a transversal so that…
Corresponding angles are , then the lines are parallel
Corresponding Angle Converse
Alternate Interior angles are , then the lines are parallel
Alt. Int. Angle Converse.
Alternate Exterior angles are  , then the lines are parallel
Alt. Ext Angle Converse
Consecutive Interior angles are Supplementary , then the lines are parallel
Con. Int. Angle Converse

4. Is It Possible to Prove That Lines P and Q Are Parallel
Is It Possible to Prove That Lines P and Q Are Parallel? If So Explain How.
Yes
m1 = 124 (vert.  thm.)
1 and 56 are supplementary
Cons. Int. Angle Converse 1
Yes
= 132
Corresponding Angle Converse

5. Is It Possible to Prove That Lines P and Q Are Parallel
Is It Possible to Prove That Lines P and Q Are Parallel? If So Explain How.
Yes
m1 = 180 – 48 – 53 = 79
1 and 79 are congruent
Alt. Int. Angle Converse 1

6. Find the Value of x That Makes p // q
For p // q, Alt. Ext. Angles must be .
4x = 3x + 30
x = 30
For p // q, Cons. Int. Angles must be Supplementary.
x + 3x + 24 = 180
4x + 24 = 180
4x = 156
x = 39

7. Find the Value of x That Makes p // q
For p // q, Alt. Int. Angles must be .
2x + 50 = 5x – 10
60 = 3x
20 = x

8. Give the Choice or Choices That Makes the Statement True
If two lines are cut by a transversal so that alternate interior angles ___________, then the lines are parallel.
If two lines are cut by a transversal so that consecutive interior angles ___________, then the lines are parallel.
Congruent
Supplementary

9. Give the Choice or Choices That Makes the Statement True
If two lines are cut by a transversal so that ____________________ are congruent, then the lines are parallel.
alternate interior angles, Alt ext, corres

10. Complete the Two Column Proof
Given
Corres.  Postulate
Given
Transitive
Alt. Ext  Converse

11. Write a two column proof
Statements Reasons
1. Given
1. l // m, 1  2
2. 1  3
2. Corres.  Postulate
3. Transitive
3. 2  3
4. a // b
4. Corres.  Converse