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Mastering Parallel Lines Theorems with Examples

Learn how to prove lines are parallel using angle relationships and the corresponding, alternate interior, alternate exterior, and consecutive interior angles converses. Practice with examples to solidify your understanding.

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Mastering Parallel Lines Theorems with Examples

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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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