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Proving Lines are Parallel

What theorems/postulates have we learned about parallel lines?. Corresponding Angles Postulate? If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.Alternate Interior Angles Theorem? If two parallel lines are cut by a transversal, then the pairs of a

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Proving Lines are Parallel

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    1. Proving Lines are Parallel You will be able to determine and prove that lines are parallel.

    2. What theorems/postulates have we learned about parallel lines? Corresponding Angles Postulate? If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Alternate Interior Angles Theorem? If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. Alternate Exterior Angles Theorem? If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. Consecutive Interior Angles Theorem? If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary .

    3. Given the previous information, can you determine that any of the following lines are parallel? 73 73 What assumption about the theorem are you making?

    4. Think back If you have a conditional statement that you know is true, which of the following do you know is true? Inverse, Converse, or Contrapositive So given a true statement: Alternate Exterior Angles Theorem: IF two parallel lines are cut by a transversal, THEN the pairs of alternate exterior angles are congruent. What is the converse, and is it necessarily true? Converse: IF two lines are cut by a transversal and the pairs of alternate exterior angles are congruent, then the two lines are parallel.

    5. Here are the converses: Postulate 16: Corresponding Angles Converse If two lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel. Since this statement is a Postulate, it does not need to be proven and can be assumed to be true.

    6. Theorem 3.8 Alternate Interior Angles Converse If two lines are cut by a transversal so that alternate interior angles are congruent, then the lines are parallel.

    7. Theorem 3.9 Consecutive Interior Angles Converse If two lines are cut by a transversal so that consecutive interior angles are supplementary, then the lines are parallel.

    8. Theorem 3.10 Alternate Exterior Angles Converse If two lines are cut by a transversal so that alternate exterior angles are congruent, then the lines are parallel.

    9. Homework p.153-154 #10-28

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