1. Proving Lines Parallel
Lesson 3-5
Proving Lines Parallel

2. Standardized Test Practice:
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)
Which of the following describes the line y = –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. Standardized Test Practice:
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
Which of the following describes the line y = –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. Postulates & Theorems To Prove Lines Parallel1 2 k 3 4 5 6 l 7 8
Postulate/ Theorem
Statement
Examples
Postulate 3.4
If two lines in a plane are cut by a transversal so that corresponding angles are congruent, then the lines are parallel
If 1  5 or 2  6 or 3  7 or 4  8, then k || l
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
None illustrated
Theorem 3.5
If two lines in a plane are cut by a transversal so that a pair of alternate exterior angles are congruent, then the lines are parallel
If 1  8 or 2  7, then k || l
Theorem 3.6
If two lines in a plane are cut by a transversal so that a pair of consecutive interior angles are supplementary, then the lines are parallel
If m3 + m5 = 180° or m4 + m6 = 180°, then k || l
Theorem 3.7
If two lines in a plane are cut by a transversal so that a pair of alternate interior angles are congruent, then the lines are parallel
If 3  6 or 4  5, then k || l

7. Determine which lines, if any, are parallel.
consecutive interior angles are supplementary. So,
consecutive interior angles are not supplementary. So, c is not parallel to a or b.
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. Alternate exterior angles
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. Original equation Simplify. Answer:
Examine Verify the angle measure by using the value of x to find Since
Answer:

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 : 4, 7, 13-16, 27, 29, 31