1. Splash Screen

2. Five-Minute Check (over Lesson 3–4) Then/Now
Postulate 3.4: Converse of Corresponding Angles Postulate
Postulate 3.5: Parallel Postulate
Theorems: Proving Lines Parallel
Example 1: Identify Parallel Lines
Example 2: Standardized Test Example
Example 3: Real-World Example: Prove Lines Parallel
Lesson Menu

3. A B C D containing the point (5, –2) in point-slope form? A. B. C. D.
5-Minute Check 1

4. What is the equation of the line with slope 3 containing the point (–2, 7) in point-slope form?
A. y = 3x + 7
B. y = 3x – 2
C. y – 7 = 3x + 2
D. y – 7 = 3(x + 2) A B C D
5-Minute Check 2

5. What equation represents a line with slope –3 containing the point (0, 2.5) in slope-intercept form?
A. y = –3x + 2.5
B. y = –3x
C. y – 2.5 = –3x
D. y = –3(x + 2.5) A B C D
5-Minute Check 3

6. A B C D containing the point (4, –6) in slope-intercept form? A. B. C.
5-Minute Check 4

7. What equation represents a line containing points (1, 5) and (3, 11)?
A. y = 3x + 2
B. y = 3x – 2
C. y – 6 = 3(x – 2)
D. y – 6 = 3x + 2 A B C D
5-Minute Check 5

8. A. B. C. D. A B C D
5-Minute Check 6

9. Recognize angle pairs that occur with parallel lines.
You used slopes to identify parallel and perpendicular lines. (Lesson 3–3)
Recognize angle pairs that occur with parallel lines.
Prove that two lines are parallel.
Then/Now

10. Concept

11. Concept

12. Concept

13. 1 and 3 are corresponding angles of lines a and b.
Identify Parallel Lines
A. Given 1  3, is it possible to prove that any of the lines shown are parallel? If so, state the postulate or theorem that justifies your answer.
1 and 3 are corresponding angles of lines a and b.
Answer: Since 1  3, a║b by the Converse of the Corresponding Angles Postulate.
Example 1

14. 1 and 4 are alternate interior angles of lines a and c.
Identify Parallel Lines
B. Given m1 = 103 and m4 = 100, is it possible to prove that any of the lines shown are parallel? If so, state the postulate or theorem that justifies your answer.
1 and 4 are alternate interior angles of lines a and c.
Answer: Since 1 is not congruent to 4, line a is not parallel to line c by the Converse of the Alternate Interior Angles Theorem.
Example 1

15. A. Given 1  5, is it possible to prove that any of the lines shown are parallel?
A. Yes; ℓ ║ n
B. Yes; m ║ n
C. Yes; ℓ ║ m
D. It is not possible to prove any of the lines parallel. A B C D
Example 1

16. B. Given m4 = 105 and m5 = 70, is it possible to prove that any of the lines shown are parallel?
A. Yes; ℓ ║ n
B. Yes; m ║ n
C. Yes; ℓ ║ m
D. It is not possible to prove any of the lines parallel. A B C D
Example 1

17. Find ZYN so that || . Show your work.
Read the Test Item From the figure, you know that mWXP = 11x – 25 and mZYN = 7x You are asked to find mZYN.
Example 2

18. m WXP = m ZYN Alternate exterior angles
Solve the Test Item WXP and ZYN are alternate exterior angles. For line PQ to be parallel to MN, the alternate exterior angles must be congruent. So mWXP = mZYN. Substitute the given angle measures into this equation and solve for x. Once you know the value of x, use substitution to find mZYN.
m WXP = m ZYN Alternate exterior angles
11x – 25 = 7x + 35 Substitution
4x – 25 = 35 Subtract 7x from each side.
4x = 60 Add 25 to each side.
x = 15 Divide each side by 4.
Example 2

19. Now use the value of x to find mZYN.
mZYN = 7x + 35 Original equation
= 7(15) + 35 x = 15
= 140 Simplify.
Answer: mZYN = 140
Check Verify the angle measure by using the value of x to find mWXP.
mWXP = 11x – 25
= 11(15) – 25
= 140
Since mWXP = mZYN, mWXP  mZYN and ||
Example 2

20. A B C D ALGEBRA Find x so that || . A. x = 60 B. x = 9 C. x = 12
Example 2

21. Homework p – 20 even