1 / 18

3.4 Proving Lines are Parallel

3.4 Proving Lines are Parallel. Mrs. Spitz Fall 2005. Standard/Objectives:. Standard 3: Students will learn and apply geometric concepts Objectives: Prove that two lines are parallel.

salena
Télécharger la présentation

3.4 Proving Lines are Parallel

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. 3.4 Proving Lines are Parallel Mrs. Spitz Fall 2005

  2. Standard/Objectives: Standard 3: Students will learn and apply geometric concepts Objectives: • Prove that two lines are parallel. • Use properties of parallel lines to solve real-life problems, such as proving that prehistoric mounds are parallel. • Properties of parallel lines help you predict.

  3. HW ASSIGNMENT: • 3.4--pp. 153-154 #1-28 Quiz after section 3.5

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

  5. 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.

  6. 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.

  7. 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.

  8. Prove the Alternate Interior Angles Converse Given: 1  2 Prove: m ║ n 3 m 2 1 n

  9. Statements: 1  2 2  3 1  3 m ║ n Reasons: Given Vertical Angles Transitive prop. Corresponding angles converse Example 1: Proof of Alternate Interior Converse

  10. Proof of the Consecutive Interior Angles Converse Given: 4 and 5 are supplementary Prove: g ║ h g 6 5 4 h

  11. Paragraph Proof You are given that 4 and 5 are supplementary. By the Linear Pair Postulate, 5 and 6 are also supplementary because they form a linear pair. By the Congruent Supplements Theorem, it follows that 4  6. Therefore, by the Alternate Interior Angles Converse, g and h are parallel.

  12. Solution: Lines j and k will be parallel if the marked angles are supplementary. x + 4x = 180  5x = 180  X = 36  4x = 144  So, if x = 36, then j ║ k. Find the value of x that makes j ║ k. 4x x

  13. Using Parallel Converses:Using Corresponding Angles Converse SAILING. If two boats sail at a 45 angle to the wind as shown, and the wind is constant, will their paths ever cross? Explain

  14. Solution: Because corresponding angles are congruent, the boats’ paths are parallel. Parallel lines do not intersect, so the boats’ paths will not cross.

  15. Example 5: Identifying parallel lines Decide which rays are parallel. H E G 58 61 62 59 C A B D A. Is EB parallel to HD? B. Is EA parallel to HC?

  16. Example 5: Identifying parallel lines Decide which rays are parallel. H E G 58 61 B D • Is EB parallel to HD? mBEH = 58 m DHG = 61 The angles are corresponding, but not congruent, so EB and HD are not parallel.

  17. Example 5: Identifying parallel lines Decide which rays are parallel. H E G 120 120 C A • B. Is EA parallel to HC? m AEH = 62 + 58 m CHG = 59 + 61 AEH and CHG are congruent corresponding angles, so EA ║HC.

  18. Conclusion: Two lines are cut by a transversal. How can you prove the lines are parallel? Show that either a pair of alternate interior angles, or a pair of corresponding angles, or a pair of alternate exterior angles is congruent, or show that a pair of consecutive interior angles is supplementary.

More Related