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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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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.

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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.

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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.

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

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

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Ex.7: Given: Prove: pq

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

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Ex.9: Given: Prove:

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

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

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Ex.12: Given: Prove:

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