Chapter 3.3 Notes: Prove Lines are Parallel

1
Chapter 3.3 Notes Prove Lines are Parallel

• Goal You will use angle relationships to prove
  that lines are parallel.

2

• Postulate 16 Corresponding Angles Converse
• If two lines are cut by a transversal so that
  corresponding angles are congruent, then the
  lines are parallel.
• Ex.1 Find the value of x that makes mn.

3

• Ex.2 Is there enough information in the diagram
  to conclude that mn? Explain.
• Theorem 3.4 Alternate Interior Angles Converse
• If two lines are cut by a transversal so that
  alternate interior angles are congruent, then the
  lines are parallel.

4

• Theorem 3.5 Alternate Exterior Angles Converse
• If two lines are cut by a transversal so that
  alternate exterior angles are congruent, then the
  lines are parallel.
• Theorem 3.6 Consecutive Interior Angles Converse
• If two lines are cut by a transversal so that
  consecutive interior angles are supplementary,
  then the lines are parallel.

5

• Can you prove that lines a and b are parallel?
  Explain why or why not.
• Ex.3 Ex.4
• Ex.5

6

• Ex.6 Find the value of y that makes ab.
• (5y 6)o
• 121o

7

• Ex.7 Given
• Prove pq

8
(No Transcript)
9

• Ex.8 Given
• Prove r p

10

• Ex.9
• Given
• Prove

11

• Ex.10
• Given
• Prove and are supplementary.
• 
  1 p
• 
  3
• 2
  q

12

• Ex.11
• Given are
  supplementary
• Prove l m

13

• Ex.12
• Given
• Prove