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Lesson 3-5

Lesson 3-5. Proving Lines Parallel. Transparency 3-5. 5-Minute Check on Lesson 3-4. Write an equation in point-slope form for each line . 1. line with slope ¾ containing (5, –2) 2. line parallel to the line 3x – y = 6 that contains (–2, 7)

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Lesson 3-5

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  1. Lesson 3-5 Proving Lines Parallel

  2. Transparency 3-5 5-Minute Check on Lesson 3-4 Write an equation in point-slope form for each line. 1. line with slope ¾ containing (5, –2) 2. line parallel to the line 3x – y = 6 that contains (–2, 7) Write an equation in slope-intercept form for each line. 3. line with slope –3 containing (0, 2.5) 4. line with slope –1/2 containing (4, –6) 5. line through (1, 5) and (3, 11) 6. Which of the following describes the liney = –2/3x + 6? Standardized Test Practice: A parallel to the line y = 3/2x + 6 B perpendicular to the line y = –3/2x + 6 C x-intercept is 6; y-intercept is 9 D x-intercept is 9; y-intercept is 6

  3. Transparency 3-5 5-Minute Check on Lesson 3-4 Write an equation in point-slope form for each line. 1. line with slope ¾ containing (5, –2) y + 2 = ¾(x – 5) 2. line parallel to the line 3x – y = 6 that contains (–2, 7) y – 7 = 3(x + 2) Write an equation in slope-intercept form for each line. 3. line with slope –3 containing (0, 2.5) y = –3x + 2.5 4. line with slope –1/2 containing (4, –6) y = –1/2x – 4 5. line through (1, 5) and (3, 11) y = 3x + 2 6. Which of the following describes the liney = –2/3x + 6? Standardized Test Practice: A parallel to the line y = 3/2x + 6 B perpendicular to the line y = –3/2x + 6 C x-intercept is 6; y-intercept is 9 D x-intercept is 9; y-intercept is 6

  4. Objectives • Recognize angle conditions that occur with parallel lines • Prove that two lines are parallel based on given angle relationships

  5. Vocabulary • No new vocabulary words or symbols

  6. t Postulates & Theorems To Prove Lines Parallel 1 2 k 4 3 5 6 l 7 8

  7. consecutive interior angles are supplementary. So, consecutive interior angles are not supplementary. So, c is not parallel to a or b. Determine which lines, if any, are parallel. Answer:

  8. Determine which lines, if any, are parallel. Answer:

  9. ALGEBRA Find x and mZYN so that Explore From the figure, you know that and You also know that are alternate exterior angles.

  10. 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 Solve Alternate exterior angles Substitution Subtract 7x from each side. Add 25 to each side. Divide each side by 4.

  11. Examine Verify the angle measure by using the value of x to find Since Answer: Original equation Simplify.

  12. ALGEBRA Find x and mGBA so that Answer:

  13. Answer:

  14. Answer: Since the slopes are not equal, r is not parallel to s.

  15. Summary & Homework • Summary: • When lines are cut by a transversal, certain angle relationships produce parallel lines • Congruent corresponding angles • Congruent alternate interior angles • Congruent alternate exterior angles • Supplementary consecutive interior angles • Homework: pg 154-155: 4, 7, 13-16, 27, 29, 31

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