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Chapter 3.3 Notes: Prove Lines are Parallel Goal: You will use angle relationships to prove that lines are parallel.

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Presentation on theme: "Chapter 3.3 Notes: Prove Lines are Parallel Goal: You will use angle relationships to prove that lines are parallel."— Presentation transcript:

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 121 o

7 Ex.7: Given: Prove: pq

8

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:


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