1 / 9

Lesson 2 - 5

Proving Lines Parallel. Lesson 2 - 5. Proving Lines Parallel - Postulates & Theorems. If two lines are cut by a transversal and corresponding angles are congruent , then the lines are parallel. Proving Lines Parallel - Postulates &Theorems.

jena-sykes
Download Presentation

Lesson 2 - 5

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. Proving Lines Parallel Lesson 2 - 5 Lesson 2-5: Proving Lines Parallel

  2. Proving Lines Parallel - Postulates & Theorems • If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. Lesson 2-5: Proving Lines Parallel

  3. Proving Lines Parallel - Postulates &Theorems • If two lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel. Lesson 2-5: Proving Lines Parallel

  4. Proving Lines Parallel - Postulates &Theorems • If two lines are cut by a transversal and consecutive interior angles are supplementary, then the lines are parallel. Lesson 2-5: Proving Lines Parallel

  5. Proving Lines Parallel - Postulates &Theorems • If two lines are cut by a transversal and consecutive exterior angles are supplementary, then the lines are parallel. Lesson 2-5: Proving Lines Parallel

  6. Theorem 3.8 (AIA Converse): If 2 lines are cut by a transversal so that AIA are congruent then the lines are parallel. Proving AIA Converse Given: 1  2 Prove: p q 3 p 1 2 q Statements Reasons 1. 1  2 1. Given 2. Vert. ’s Theorem 2. 1  3 3. Trans. POC 3. 2  3 4. Corres. ’s Converse 4. p q

  7. Theorem 3.9 (CIA Converse): If 2 lines are cut by a transversal so that CIA are supplementary then the lines are parallel. Proving CIA Converse p Given: Angles 4 and 5 are supplementary. Prove: p and q are parallel 6 5 4 q Reasons Statements 1. 4 and 5 are supplementary. 1. Given 2. 5 and 6 are supplementary. • Linear Pair Postulate 3.  Supplements Theorem 3. 4 6 4. p q 4. AIA Converse

  8. 2. 1. 3. 4. Examples: Proving Lines Parallel • Find the value of x which will make lines a and lines b parallel. Answers: 1. 20° 2. 50° 3. 90° 4. 20° Lesson 2-5: Proving Lines Parallel

  9. Ways to Prove Two Lines Parallel • Show that corresponding angles are equal. • Show that alternative interior angles are equal. • Show that consecutive interior angles are supplementary. • Show that consecutive exterior angles are supplementary. • In a plane, show that the lines are perpendicular to the same line. Lesson 2-5: Proving Lines Parallel

More Related