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Chapter 3.3 Notes: Prove Lines are Parallel

Chapter 3.3 Notes: Prove Lines are Parallel. Goal: You will use angle relationships to prove that lines are parallel. Postulate 16 Corresponding Angles Converse : If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.

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Chapter 3.3 Notes: Prove Lines are Parallel

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  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 m║n.

  3. Ex.2: Is there enough information in the diagram to conclude that m║n? 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 a║b. (5y+ 6)o 121o

  7. Ex.7: Given: Prove: p║q

  8. Ex.8: Given: Prove: r || p

  9. Ex.9: Given: Prove:

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

  11. Ex.11: Given: are supplementary Prove: l || m

  12. Ex.12: Given: Prove:

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