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September 29, 2014

September 29, 2014. Take out your homework, do not turn in Get ready for a warm-up. Warm-up.

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September 29, 2014

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  1. September 29, 2014 Take out your homework, do not turn in Get ready for a warm-up

  2. Warm-up The maze below has two intersecting sets of parallel paths. A mouse makes five turns in the maze to get to a piece of cheese. Follow the mouse’s path through the maze. What are the degrees at each turn?

  3. Proving Lines Are Parallel So far we have been looking at angle pair relationships based upon the fact two lines are parallel and cut by a transversal. What we will look at today are the converses. This means we are trying to show two lines are parallel based upon information given about the angles.

  4. Converses… Corresponding Angles Converse If two lines are cut by a transversal so the corresponding angles are congruent, then the lines are parallel Alternate Interior Angles Converse If two lines are cut by a transversal so the alternate interior angles are congruent, then the lines are parallel Same-Side Interior Angles Converse If two lines are cut by a transversal so the same-side interior angles are supplementary, then the lines are parallel. Alternate-Exterior Angles Converse If two lines are cut by a transversal so the alternate exterior angles are congruent, then the lines are parallel.

  5. How we use them… Ex 1. Find the value of x that makes m||n 3x + 5 = 65 3x = 60 x = 20

  6. Example 2 Is there enough information to conclude m||n? Yes, because you can find the angle supplementary with the given angles. 75 Then the corresponding angle converse allows us to conclude that the lines are parallel.

  7. Know the difference? What is the difference between what you can prove with the Corresponding Angles Converse and the Corresponding Angles Postulate. The converse proves the lines are parallel. The postulate is for proving the angles are congruent.

  8. Example 3 Can you prove that a||b? Why or why not? a. b. 1 2 Yes, the alternate exterior angles converse No, supplementary angles don’t have to be congruent

  9. Example 4 In the figure, r||s, and angle 1 is congruent to angle 3. Prove p||q. Statements Reasons 1. r||s 1. Given 2. 2. Corres. Angl. Post 3. Given 4. Transitive Prop. Of Congruence 5. p||q 5. Alternate Interior Angles Converse

  10. HOMEWORK: #’s 1-6 all, 9-21 odds

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