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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 m║n.

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**Ex. 2: Is there enough information in the diagram to conclude that m║n**

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.

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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 a║b. (5y+ 6)o 121o **

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Ex.7: Given: Prove: p║q

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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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3.4 Proving Lines Parallel Converse of 3.3. Theorems to find Parallel lines If two lines are cut by a transversal and corresponding angle are congruent,

3.4 Proving Lines Parallel Converse of 3.3. Theorems to find Parallel lines If two lines are cut by a transversal and corresponding angle are congruent,

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