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Lesson 3-5 Proving Lines Parallel

Lesson 3-5 Proving Lines Parallel. Postulate 3.4- If two lines are cut by a transversal so that the corresponding angles are congruent, then the lines are parallel. Example: Postulate 3.5- Parallel Postulate

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Lesson 3-5 Proving Lines Parallel

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  1. Lesson 3-5 Proving Lines Parallel • Postulate 3.4- If two lines are cut by a transversal so that the corresponding angles are congruent, then the lines are parallel. Example: • Postulate 3.5- Parallel Postulate If a given line and a point not on the line, then there exists exactly one line through the point that is parallel to the given line.

  2. Proving Lines Parallel

  3. consecutive interior angles are supplementary. So, consecutive interior angles are not supplementary. So, c is not parallel to a or b. Example 5-1a Determine which lines, if any, are parallel. Answer:

  4. Example 5-1b Determine which lines, if any, are parallel. Answer:

  5. ALGEBRA Find x and mZYN so that Explore From the figure, you know that and You also know that are alternate exterior angles. Example 5-2a

  6. Plan For line PQ to be parallel to MN, the alternate exterior angles must be congruent. Substitute the given angle measures into this equation and solve for x. Once you know the value of x, use substitution to find Example 5-2b Solve Alternate exterior angles Substitution Subtract 7x from each side. Add 25 to each side. Divide each side by 4.

  7. Examine Verify the angle measure by using the value of x to find Since Answer: Example 5-2c Original equation Simplify.

  8. ALGEBRA Find x and mGBA so that Answer: Example 5-2d

  9. Given: Prove: Example 5-3e

  10. Statements Reasons 1. 1. Given 2. . 2. Consecutive Interior Thm. 3. 3. Def. of suppl. s 4. Def. of congruent s 4. 5. 5. Substitution 6. . 6. Def. of suppl. s 7. 7. If cons. int. s are suppl., then lines are . Example 5-3f Proof:

  11. Given: Prove: Example 5-3g

  12. Proof: Statements Reasons 1. 1. Given 2. 2. Alternate Interior Angles 3. 3. Substitution 4. . 4. Definition of suppl. s 5. 5. Definition of suppl. s 6. 6. Substitution 7. 7. If cons. int. s are suppl., then lines are . Example 5-3h

  13. Answer: Example 5-4a

  14. Example 5-4b Answer: Since the slopes are not equal, r is not parallel to s.

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