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Geometry 3.3

Geometry 3.3 . Proving Lines Parallel. Learning Target. Students should be able to… Use the angles formed by a transversal to prove two lines are parallel. Warm-up. Homework Check. Homework Check. Homework Check. Homework Check. Homework Check. Homework Check.

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Geometry 3.3

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  1. Geometry 3.3 Proving Lines Parallel

  2. Learning Target • Students should be able to… • Use the angles formed by a transversal to prove two lines are parallel.

  3. Warm-up

  4. Homework Check

  5. Homework Check

  6. Homework Check

  7. Homework Check

  8. Homework Check

  9. Homework Check

  10. Review…What is a converse? A converse is found by switching the hypothesis and the conclusion. Switch the “if” and the “then” statement. The converse does not have to be true.

  11. Practicing Converse Statements Original Statement: If my dog is a Dalmatian, then it has spots. Converse Statement: If my dog has spots, then it is a Dalmatian. Is the converse true???

  12. Practicing Converse Statements Original Statement: If it is sunny outside, then it won’t rain. Converse Statement: If it won’t rain, then it will be sunny outside. Is the converse true???

  13. Practicing Converse Statements Original Statement: If my cell phone is turned off, then it will not ring. Converse Statement: If my cell phone will not ring, then it is turned off. Is the converse true???

  14. Practicing Converse Statements Do you have a statement to try? Original Statement: Converse Statement: Is the converse true???

  15. Connecting Today we are using the converse with the theorems or postulates we discovered yesterday in section 3-2. Who can remember what any of the theorems or postulates were yesterday?

  16. Corresponding Angles Postulate Corresponding Angles Postulate: If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. Converse of the Corresponding Angles Postulate: If two coplanar lines are cut by a transversal so that a pair of corresponding angles are congruent, then the two lines are parallel.

  17. Alternate Interior Angles Theorem Alternate Interior Angles Postulate: If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. Converse of the Corresponding Angles Postulate: If two coplanar lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the two lines are parallel.

  18. Alternate Exterior Angles Theorem Alternate Exterior Angles Postulate: If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent. Converse of the Corresponding Angles Postulate: If two coplanar lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then the two lines are parallel.

  19. Same-Side Interior Angles Theorem Alternate Exterior Angles Postulate: If two parallel lines are cut by a transversal, then the two pairs of same-side interior angles are supplementary. Converse of the Corresponding Angles Postulate: If two coplanar lines are cut by a transversal so that a pair of same-side interior angles are supplementary, then the two lines are parallel.

  20. Corresponding Angles Postulate We already know that… If two parallel lines are cut by a transversal their corresponding angles are congruent. Now we are going to look at the converse of this postulate. Converse of the Corresponding Angle Postulate: If corresponding angles are congruent, then the two lines are parallel.

  21. Corresponding Angle Postulate Examples

  22. Corresponding Angle Postulate Examples

  23. 3-3 Guided Notes Converse of the Alternate Exterior Angle Theorem Converse of the Same-Side Interior Angle Theorem Converse of the Alternate Interior Angle Theorem

  24. Examples with the Converse Theorems

  25. Examples with the Converse Theorems

  26. 3-3 Extra Practice

  27. 3-3 Extra Practice

  28. Homework Assignment • We will be having a Review/Quiz day on Monday. • It will cover 3.1 – 3.3. We will work through practice problems in class before taking the quiz. • Homework Assignment: • Page 166 – 167 #1 – 9 odd

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